Contests.
The most important high school contests in the US are those administered
by the American Mathematics
Competitions. Other contests with excellent intermediate-level problems
are the Mandelbrot
and ARML.
You can hone your solutions writing skills with the USAMTS
or the Tournament of Towns. Those of you who like doing research projects
should get involved with the Siemens Westinghouse Competition.
Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.