Competitions:
American Mathematics Competitions (AMC)
Art of Problem Solving: AMC: View previous tests and solutions
Pi Day
Puzzles:
AIMS Puzzle Corner: a collection of math and science puzzles
Brilliant: Build quantitative skills in math, science, and computer science with fun and challenging interactive explorations (paid service but it has a free trial)
Magic Squares: pdf | solution & explanation | 4 by 4 solution
Magic Triangles: pdf | online version
Games:
Tower of Hanoi: play online
Peg Jump: play online
Revseri: play online | play online | play online
Mancala: play online | play online
15-puzzle game: play online
Marble solitaire: play online
Mental Math Tricks