The Truth Tree's Math and Logic Board
Collection of math and logic puzzles ranging in levels of difficulty.
http://www.truthtree.com/mathdoor.html

TechInterview
Answers to technical interview questions, programming problems, and brain teasers.
http://www.techinterview.org/

Perplexus
A forum and collection of brain teasers, logic problems, math problems, paradoxes, science games, probability, riddles, and geometric shapes. The puzzles are searchable and categorized, most have solutions.
http://perplexus.info/

The Monty Hall Problem
A probability theory puzzle with solutions. [English and German.]
http://www.remote.org/frederik/projects/ziege/

Mathematical Jigsaw Puzzles
Information on polyominos and square puzzles.
http://home.hetnet.nl/~paslen/jigsawpuzzles.html

WU Forums
Discussion board hosted at Berkeley with talk about a variety of solved and unsolved brain teasers.
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard

Two Envelope Paradox - Solution
Claims that the two envelope paradox comes from the incorrect use of probabilities.
http://www.anc.ed.ac.uk/~amos/doubleswapsoln.html

Quick Logic Puzzles
Use the clues provided to deduce the correct sequence of numbers in the hidden code.
http://www.robertwilliams.org/qlp/index.html

The Puzzles of Oscar
Contains puzzles and games with solutions.
http://uk.geocities.com/oscarlagioia/riddles.html

Monty Hall Game
JavaScript example of the Monty Hall Game. This game demonstrates the real (empirical) affect of statistics. [Does not display correctly in all browsers.]
http://montyhallgame.shawnolson.net/

Leisure Ideas: Puzzles
Some mathematical puzzles with answers and/or a hint.
http://www.leisureideas.com/logic%20puzzles.htm

CellFighter
Shareware game based around an extension of the game of life.
http://www.cellfighter.com/conways-life-download.html

Kakuro-san
Providing graded Kakuro puzzles every day, plus old puzzles.
http://www.kakurosan.com

IBM Research: Ponder This
Monthly logic and math puzzles set by IBM researchers with solutions.
http://researchweb.watson.ibm.com/ponder/