Great Math Puzzles
Peg Solitaire

You begin with a configuration where there's a hole in the center, while all other are filled with marbles (or called pegs). You can remove a peg by jumping one over it. The goal is to leave just 1 peg on the board.

Klotski

The goal is to slide the red block into the exit position.
15 Puzzle

goal is to order the numbers by sliding the blocks.
Pentominos Puzzle Solver

Some excellent intro to polyominoes:

- Time Travel and other Mathematical Bewilderments Buy at amazon, Chapter 14. (1988) By Martin Gardner.
- Polyominoes : Puzzles, Patterns, Problems and Packings Buy at amazon by Solomon W Golomb. (2nd ed., 1996)
MineSweeper3D

http://www.software3d.com/Mines3D/ (2003-09,2006-09-01) Windows
★ MineSweeper3D by Robert Webb. It is similar to the puzzle Minesweeper that comes with Windows, but MineSweeper3D lets you play it on 3D solids. Very well done.
Books
A arresting introduction to tangrams can be found in Time Travel and other Mathematical Bewilderments , by Martin Gardner. Buy at amazon It includes a short bibliography.
If you like mathematical puzzles, you may find this book interesting [Puzzles Old and New: How to make and solve them By Jerry Slocum and Jack Boterman. Buy at amazon] The book includes photographs of many many puzzles. It gives you a panorama of all types of physical puzzles.