List of United States middle school mathematics competitions

National middle school mathematics competitions

AMC 8 hosted by the American Mathematics Competitions is a very large middle school math contest taken in-school. (website)
American Scholastic Mathematics Association (ASMA)
Archimedean Challenge #1
Continental Mathematics League (website)
Game-a-thon challenges students to design and build math games in this national contest.
MATHCOUNTS is perhaps the largest and well-known middle school math contest. (website)
Mathematical Olympiads for Elementary and Middle Schools (MOEMS) is a very large elementary and middle school math competition. (website)
The Math Bee hosted by the North South Foundation
Math League has different names in different states and regions.
Noetic Learning Math Contest: a popular problem-solving contest for students in grades 2-8.
Online Math League (OML)
Perennial Math
mathleague.org -- elementary, middle, high school. (website)
National Trimathlon is a math competition for kids in grades 3 through 6.
Russian School of Mathematics Foundation International Math Contest is a two-round Olympiad-style contest for students in grades 3-8 (website)

Art of Problem Solving Books -- Introductory subject texts and Art of Problem Solving Volume 1 are usually recommended for middle school math team students.
Mathematical Olympiads for Elementary and Middle Schools (MOEMS) publishes two problem solving books.
MathCounts produces new material annually, some of which is available here.

Art of Problem Solving Classes -- Introductory classes are usually recommended.
Education Program for Gifted Youth (EPGY) hosts online classes in mathematics and other subjects.

Art of Problem Solving (AoPS) is a vast resource for avid students of mathematics. Free resources at AoPS include articles, middle school math forums, blogs, Math Jams, the AoPSWiki, and much more.
The Math Forum at Drexel University is a very large math site with a lot of great content.