MCML is the organization that runs our monthly meets. Here's their webpage with practice problems organized by month. Click on the month you prefer, then on the topics that you want to practice.
https://sites.google.com/site/monroecountymathleague/resources
The AMC is the first contest on the Math Olympiad track. Participants who perform well can qualify for the AIME, then the USAMO, and ultimately the IMO. Below is a link to the website for the AMC, where you can find practice problems for the AMC 8, 10 and 12, with official and alternate solutions.
http://www.maa.org/math-competitions
http://www.artofproblemsolving.com/Wiki/index.php/AMC_Problems_and_Solutions
Here are high-level math problems from ARML. They are difficult, but worth solving!