THINKS.COM says, "The Internet's most entertaining puzzles are here." They have, among other things, math puzzles, picture puzzles, logic puzzles, chess puzzles, and sudoku puzzles.

http://thinks.com/puzzles/

     BRAIN GYM: Don't feel bad if you flunk brain gym: these are trick questions.

http://www.naute.com/puzzles/puzzle9.phtml

SIMPLE TO SERIOUSLY DIFFICULT PUZZLES

     YAHOO has a whole section of its vast empire given to puzzles. Find here puzzles for many levels of ability and many interests:

http://games.yahoo.com/puzzle-games

     The GREY LABYRINTH is for serious puzzlers. These will give you a tremendous mental workout.

http://www.greylabyrinth.com/puzzles

     RUBIK'S CUBE SOLUTIONS: Actually, there are several solutions laid out here, and you can use any of them. You say you threw your cube away in disgust? I see an ad on the site advertising an electronic Rubik’s cube, and I'm sure Google knows where you can buy an actual, physical one.

http://www.chessandpoker.com/rubiks-cube-solution.html

JIGSAWS AND OTHER PICTURE PUZZLES

     Find here the Internet version of a whole raft of picture puzzles - all free, all calibrated to be easy, medium, or difficult. The puzzles are meant for grownups, but older kids will like them too. And there must be about a hundred, with more coming along all the time.

http://www.allstarpuzzles.com/picture/index.html

     JIGZONE was recommended to us by reader Helen Jones, and our thanks go to her. Here you can play with jigsaw puzzles, which apparently improve your spatial relationships. And you can make jigsaw puzzles from your photos, or from the pictures JIGZONE supplies. I was surprised to find that their puzzle of the day – one of many they supply – was an actual, traditional jigsaw, rather than the straight-cut pieces I had encountered at other sites. They're put together online, though, and need to be shared online. But, let's say you took photos of a party or a weekend with friends. You could turn your photos into an online puzzle as a thank-you gift to them, assuming they're online too.

http://www.jigzone.com/

     If, on the other hand, you'd like to turn a photo into a traditional cardboard-backed puzzle, here's how:

http://www.associatedcontent.com/article/22507/
how_to_make_a_jigsaw_puzzle.html

     And to make a wooden jigsaw puzzle:

http://www.newpuzzles.com/instructions.htm