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.
American Scholastic Mathematics Association (ASMA)
Continental Mathematics League
Homeschool Math Contests has a chart of math contests open to individuals (homeschoolers and otherwise), and also an up-to-date state-by-state list of regional meets.
Kumon Math Challenge
MathCounts is perhaps the largest and well-known middle school math contest.
Mathematical Olympiads for Elementary and Middle Schools (MOEMS) is a very large elementary and middle school math competition.
The Math Bee hosted by the North South Foundation
Math League has different names in different states and regions.
Online Math League (OML)

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.