Puzzles

http://www.mathpuzzle.com/ is fantastic! Constantly updated with everything happening in recreational mathematics.

Another great puzzle site: http://www.stetson.edu/~efriedma/puzzle.html

No list of puzzles sites would be complete without raving about the MIT Mystery Hunt

Sequence Puzzles

I have several sequence puzzles, so they have their own page.

Magic Squares

I used the magic square puzzle when talking about Benjamin Franklin.

Clickmazes has all sorts of state mazes, including a 5x5 step-over maze the cub scouts have enjoy.

Polyomino Addition

Polyomino are shapes made out of a certain number of (usually) squares. For example, a set of pentaminos consists of all the shapes one can make out of 5 squares. The usual puzzle is to fit them into some shape, such as a rectangle.

Polyomino Addition is a fun twist on polyominos. Given 2 different sets of polyominos (2-4 pieces in each set of 3- 4- or 5-ominos), the challenge is to find a shape which both sets can make.

http://www.stetson.edu/%7Eefriedma/polyadd/

Japanese puzzles

Deductive Logic puzzles are very popular in Japan. It is believed that doing a puzzle each day will keep the mind healthy and reduce the risk of senility and parkinson's disease.

Sudoku

This is a simple and very popular deductive logic game. It is played with numbers but is not a math puzzle, since it could just as easily be played with the letters A-I. Fairly good range of difficulty.

http://www.playr.co.uk/sudoku/index.php

SlitherLink

I like this puzzle. It has good depth for difficult puzzles, and a lot of patterns which can be recognized.

http://www.puzzle-loop.com/

This site has online versions of several other Japanese puzzles as well. The largest size can be challenging.

Kakuro

This puzzle involves some actual arithmetic.

http://en.wikipedia.org/wiki/Cross_Sums

Inductive Logic Puzzles

Some Logic Puzzles on this site.

Formal Logic

Lewis Carroll was an math professor and expert in formal symbolic logic. Here are some nice puzzles: http://www.math.hawaii.edu/~hile/math100/logice.htm