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I have created a diagram of most contests and programs for high school students in Suffolk County who have interest in mathematics and/or computer science. It might be helpful for non-Suffolk students, beware some information are location sensitive.
This small list was made so no one have to walk my way anymore. I had no idea there are contest I could join until 11th grade was half over. Many of the contests require school's participation, you will have to talk to the principle (he handles the money..) and your math/computer science teacher.

These competitions are opens to high school students and most likely do-able for Suffolk students. Like there is no way a Suffolk student is going to take Rice University Mathematics Tournament without getting funds and sitting on a bus(car) for days1. All contest requires traveling are either within 200 mile radius centered in Suffolk, or there are organized trips that cut down the cost. Only contests with actual value prize or enough publicity are listed, there are a lot problem of the week/month contests, there is no way to mention them all.
The difficulty means the difficulty of individual question(ignore the time limit) or in other cases(like Intel Science Talent Search), the difficulty of gaining a high position in the contest.
Arrows means one have to do well in one contest to be accepted to join the contest arrow points to.
For more detailed information on each contest, Wikipedia it(recommended for more famous contests, usually their site sucks.) or follow the links to the official site.

Mathematics competitions
The most common ones suffolkian can encounter
The easiest math teasers: Colstate Question of The Week(Columbus State University Math Contest)
Features 4 questions every week at Monday 0:00(not exactly, usually before 0:20). Two of them are for high school students. Problem of the week and Algebra in Action. An correct entry will be chosen randomly for each contest and will be awarded with a what's your problem t-shirt.(2 chance per week)
The question are usually extremely easy, the only fun part about this simple contest would be become the first one to solve it. Person who answers the problem correctly will be listed on their site.
I wait till 0 am every time, the list of people who solved it are ordered chronically.

The most common local math contest on Suffolk: Math League.
I believe a lot of schools(at least 14) in Suffolk has a math teams compete with other schools though math league. This is like the no.1 easiest way to compete with other math students in real life. There are 6 problems, each 2 problems have a 12 minute time restriction. Problems are fairly easy and usually have an algebraic answer.

NYSML: New York State Mathematics League, require some registration fee. Usually schools will pay for you. To be selected, you have to make into Suffolk County Math Team[SCMT, unofficial abb.]. I believe it's determined by performance on math league. Local math league coaches can also nominate 2 students with the qualified students. Contest method and questions similar to ARML.

ARML: American Regions Mathematics League. Like NYSML, you have to make into the SCMT. There are a few sites for the contest, Pennsylvania State University is the site for SCMT. There will be 5 different rounds:

1. a individual round, with 10 minute time limit on 2 problems, total of 8 problems and 40 minutes.
2. A team round of 20 minutes to solve 10 problems.
3. Relay, 3 people of a team work on 3 questions one by one
4. Power, proof based problem for the entire team to solve in an hour
5. Super Relay, like relay, but with 15 people!!!!

I only got a primeth prime number(but not a primeth primeth prime number) correct out of 8 questions on 2008. Yep... that's 3 out of 8.

Monday Math Madness
Like the name suggests, the questions are posted every two Mondays. It's done by email submission.
Prize are usually $10 amazon gift card or Rubik's Revolution(which I won, and occationally there are better prizes from sponsors(I won a TI N-Spire CAS from them)
The contest either held on Wild About Math or blinkdagger.

Suffolk County Mathematics Tournament: Sponsored by Suffolk County Math Teachers Association and taking place in Suffolk County Community College. Each school can bring at most 4 teams to the contest. The fees usually are covered by individual schools instead of the students. The coach select the teams. Consist of 3 rounds and calculators are allowed in each one of them.

1. 15 questions, each grade get different one. 45 minutes to solve all 15 questions, usually have algebraic solutions.
2. 10 multiple choice questions with 5 choices. No grade distinctions.I believe it has a 30 or 25 minute time limit.2 This and the above count as individual score
3. 16 team questions for 45 minutes(I think). I believe team score counts some individual scores.

The winner will be announced shortly after the end of the team round.

The road to IMO
The most prestigious mathematic contest in the world for high school student is the International Mathematical Olympiad. There are a few paths to achieve that in US, but both have to go though AIME and USAMO.

AMC: The American Mathematics Competitions is one of the ways to get into AIME. 25 questions in 75 minutes. The top student of AMC for 4 years = one gold medal(maybe not real gold). The top 1% of AMC 10 and top 5% of AMC 12 goes into AIME. AIME have around 15000 people each year, if we assume same amount of people take AMC 10 and 12. then around half million people take AMC each year. Around 18000 people took it in NY in 2008.

USAMTS: USA Mathematical Talent Search. 5 question per month. Yeah, use any thing you want and submit your answer... average 6 days per questions, you should have perfect amount of time to do research and finish them. Asking for help from other people to solve it for you would be cheating. The proofs gets your points, the thoroughness of the proof will determine how much point you can get(max is 5). People with most points at end of the year can get a few books and other goodies. Top 30 male and female will be invited into AIME.

AIME: American Invitational Mathematics Examination. The name says clearly it's invitational. Only around 15000 people join it each year, 2006 has 22000...-.- There will be 15 questions with 3 hour time limit, the questions are hard, mode are usually 2 or 3 out of 15. Answers are integers between 0 to 999, a lucky guess gives you a winning chance.
Top 500 goes into USAMO.

USAMO: Be one of the participant of USA Mathematical Olympiad is my ultimate goal next year. It shows I'm one of the top 500 people in mathematics (currently, I'm assume I'm around the top 20000 in US). It's proof based, like IMO, except a bit easier. Below are taken directly from the official site.

The USAMO is a six question, two day, 9 hour essay/proof examination. All problems can be solved with pre-calculus methods. Approximately 500 of the top scoring AMC participants (based on a weighted average) are invited to take the USAMO. U. S. citizens and students legally residing in the United States and Canada (with qualifyng scores) are eligible to take the USAMO.

12 people will be selected to go to Washington D.C. for awards, and they will be invited into MOSP.

MOSP:
Mathematical Olympiad Summer Program is the summer program preparing for students to represent US in IMO. Out of 12 people, only 6 will be chosen. I heard it's very intense. Some notes taken from MSOP by Reid Barton can be found here.

IMO
International Mathematical Olympiad, 6 people can make up a team for a country. 9 hours in 2 days for 6 questions. It's said the 4th question are always the easiest one. There is a lot info on IMO in every language, there was even a book written about it --Count Down: The Race for Beautiful Solutions at the International Mathematical Olympiad
Gold in IMO is the Fields medal for high school students.

Other Math contests
HMMT
The Harvard-MIT Mathematics Tournament is a very difficult challenge with years the best scorer get below 50%. The award is a Klein bottle. Great way to visit a college if your future goal is MIT(obviously, because you are reading this post) or Harvard. Students can form teams with students from other schools. It usually starts in February.

PUMaC
Princeton Math Competition. I don't know much about it, but seems like the same difficulty level as HMMT. It usually take place in November, but the 2008 PUMaC are taking place on January 2009.

iTest
Prize is $200 gift card(for 2008).A team of at most 5 people have 4 days of time to finish 100 math problem. Easy questions are AMC 12 easy level, hard question are USAMO level.
It also compass an video contest, another chance to earn some money.
The top team/school on the iTest are invited to a tournament.
Top team's stats will be submitted to top colleges.

World Math Day
I don't know how it works, but it seems like for... very young kids to solve very easy problems and get enough points for the lulz. That's why I join it... to beat young kids in simple math... MUHAHAHAHAHA... starts around March of each year.

USAMTS alike
These contests are in USAMTS format, 1 month and solve a few questions and send to the grader online.
Wisconsin Mathematics Talent Search
The best scorer can compete for $24000 scholarship(for University of Wisconsin only). Do it if that's your fav school. and Honor day, but seems like for Wisconsin residents only.

Contests like the Math League
These are contests administrated like math league, in one's own school and mail in the result. Great scorers qualify for awards. I know very little about them because sadly, their official site is not user friendly at all. These are Log 1(one page description and... yep that's all there is to it), Rocket City Math League(seriously... why use flash for navigation?), The Mandelbrot Competition.

Mathematical Modeling
M3 challenge and HiMCM are the top 2. Here is what I learned from the M3 challenge. I don't like applied math, read about HiMCM yourself. But M3 challenge really beat most pure math contest... prize money is... wow!!! $20000 for the winning team!!! Applied math does earn more than pure math.
My suggestion, don't take mathematical modeling because you are good with pure math, it really doesn't help much.

some collection of not not well known or intense contests
Anyone heard of Trig-Star before? An annual competition of trigonometry questions. The questions are all calculation questions.
Plus! New Writer Award is a competition held once in 2 years. Competitor submit their mathematical writing to Project Math Minds Scholarship from the Actuarial foundation, nothing much to say about it. One of those applied math thing with no right answer. Just like all other applied math, have way more monetary award than pure math contests. I'm not sure but from what I see, only Mu Alpha Theta members are allowed to join the contest.

Computer Science competitions
St. Joseph's Annual High School Programming Contest in Long Island
My school(Shoreham Wading-river High School, SWR) participates it every year. The winning team member gets $500 each. Each time can consist from 1 to 3 people. Language allowed: C++, Java and VB. Half Hollow Hills East and Smithtown dominated the last 5 years. This year SWR will take the goal3.

USACO
Language allowed: C, C++, Java, and Pascal.
USACO have 4 parts
The USACO training program. Here, do small training problems.
Six Internet competitions, it's like the AIME for CS.
US Open, another competition similar to Internet competition, it's like the USAMO for CS.
Training camp for IOI, similar to MOSP.

IOI
The IMO of informatics(or computer science). Each country can have 4 participants. It last 2 days. Since people join computer science competition are far fewer than mathematic competitions, IOI is a lot easier than IMO, personally speaking. IMO problems are impossible to me, IOI is at least do-able. Gold in IOI is the Turing Award for high school students.

Project Euler
This is in no way a competition(there is no awards...), but I have to mention this. There a many programming contests taken online in different fields, AI, e-commerce and other stuff, but Project Euler is the No.1 place to increase both mathematical and programming skills. It is filled with challenging mathematic oriented programming problems, a new one is added every week. After finish one problem, you can browse the forum for that particular problem, where participants show others how they did it. I just wish its server is more stable, it has way too much down time.

The math League alike in computer science
ACSL
Another math league like system, but instead of math, it's computer science. Top students can get free books.

GHOP: The Google Highly Open Participation Contest are made for high school students. Google allow students to work on any of the 10 open source projects. Finish one task = a GHOP t-shirt. Each time when 3 task is done, $100 will be awarded, max $500. The person does the best job in 1 open source project gets a chance to tour Googleplex.

There is no ACM High School competition sites around Long Island area.
Other competitions for computer science? yes, there are a lot, way too much to cover, I can only point out the most important ones and the most local ones for you. Most of the contests can be taken remotely and don't have much requirements like the math competitions do.

The general contest basically saying "we will reward you for anything scientific/mathematical/technological."
Intel Science Talent Search/Siemens Competition
These 2 competition have the best website among all the competition I have mentioned, just read their site and you will know why they are the most organized and most weighted competitions around. Also they offer the most money. Also become a grand finalist is as good as getting gold on IMO. Even Intel is said to be an science competition, it rewards math and computer science scholars like Siemens Competition. It's the best value one out there(and yep, take a lot of preparation). Become a finalist is the Nobel Prize for high school students.
The non contests
For computer science genius who finished college materials, take the GRE CS Subject test.
For math genius who finished college materials, take the GRE math Subject test.
Math summer camps: MathCamp, HCSSiM, PROMYS, MOSP if you are lucky. Ask the colleges in long island about summer programs, they sometimes have good stuff.
Math Socialites: Mu Alpha Theta(I wish my school has a chapter), AMS[Member since 2008], MAA[Member since 2008].

The Master plan
Get active!

1. Make your school one of the Mu Alpha Theta chapter.
2. Make sure you can get a team of students who love math
3. Start to plan for funding
4. Print a copy of this page so you have a list of everything out there, find the dates of the competition, and register for them
5. it's actually possible to participate in every single thing I mentioned, there is no date conflict(at least in 2007-2008 period) except summer programs(if you are a freshman, then you have a chance to complete them all). But join 20 math contest... even I will call that as "having no life"

What are the ones most stand out to colleges?
The top 3: IMO, Intel, Siemens. Participate in IMO(or MOSP), Intel finalist, Siemens finalist. Almost means a free pass to any college of your choice. It's way better than a 2400 in SAT and 4.0 GPA
The nice ones: USAMO, Intel, Siemens, ARML, IOI. Participation in USAMO, IOI. Semi finalist in Intel, Siemens. One of the top individuals in ARML. These would put some weight to your college application. It's said that people participated in USAMO get into HYPS and MIT. But I know there are people who got into USAMO and getting rejected by a lot of schools due to poor GPA, SATs. Why is IOI not in the top? I personally feel all other Olympiads are much easier than IMO. Admission might like IMO a lot more than IOI. But there are only two IOI gold medalist from US last year, so it's more rare. Putting it here seems good enough.
Others:
Everything else doesn't really have as much weight as a 4.0GPA + 2400 SATs, maybe getting full credit on both GRE subject tests(that means your CS/math skill are beyond average first year graduate students) can create some good impressions. Doing well on HMMT and PUMac can definitely help if you are trying to get into their college.

Finally, this is 6 hours of work and some extra research before I started this article. Excuse my poor English. I hope you find it useful. I'm part of Suffolk County Math Team, I plan to help the community to do better academically in the future. I also hope you do fine on all competitions them, don't stress out over them. There is no way to improve one's math skill dramatically4, so do a lot of preparation when you still can(yes, I'm talking to you, freshman).

There is a great site to investigate for more:
Home School Math Contests

Before purchasing homes for sale, learn to use your debit cards and in this regard apply for health insurance well in advance, so that you don’t have to go for low interest mortgage deals.

1. 1. unless you are super rich, of course, then you don't need this article. You can find a lot more on Wikipedia
2. 2. I can't remember, and the association should have a better website
3. 3. Very reasonable prediction
4. 4. Well there is always one way to improve skills dramatically, seal oneself in a room with all the math material one need and block all the possible escape routes. Food and drinks will be provided. Do that for 14 hours on weekends and 8 hours on normal days seems to create geniuses. I know someone did that for piano and now a musician. But, not recommended at all due to high risk of permanent psychological damage.