Here is a page of puzzles I own.

In general, there are several criteria I look at:

• elegance: Probably the most important. Elegance means that the solution is difficult to find, but once found, it is clean and obvious. Re-solving the puzzle should not take undue time, and dexterity should have little relevance. (You won't know for sure unless you solve it first, but in many cases, you can guesstimate. This probably has an elegant solution, this probably does not.) Generally speaking, assembly and disentanglement tend to be more elegant, whereas labyrinths, transposer, tantrix, arrangement, dexterity and non-symmetrical assembly tend to be less so.

• aesthetics: Puzzles that look good are preferred, as I have a bunch displayed. I live in an apartment, so compactness is also nice.

• difficulty: More difficult puzzles are preferred. However, difficult puzzles are easy to find: just go and grab a rubic's cube or an arbitrarily complex chinese patience puzzle. Elegance and aesthetics are more appreciated.

Some examples of puzzles I think I'd enjoy.

• Hanayama Cast Metal, some of which are very pretty: Chain, Disk, Flag, Coaster.

• Assembly: Triple Cross, Hypbrid, Classic Set, Sattelite, Dovetail Burr.

• Disentanglement: Parallel Dimensions (I've solved this one but don't have it - it looks a bit ugly/B&D but has a ridiculously elegant solution.), Wise Guy, Big Shot, Triple Play. If I were a girl, the solvable ones of these would be perfect.

Unfortunately, puzzles seem more popular in other countries, but here are some places you can order puzzles online:

• Puzzlemaster (Canada)
• Potty Puzzles (UK)
• Faze 3 (UK)
• Cleverwood
• Livewire Puzzles (Canada)
• Frik n Frak
• Bits & Pieces (Not recommended: seems to carry poor-quality puzzles.)
• Cast Puzzle (Japan - Hanayama Puzzles) (These can be found in other stores, and many of them rank high on the aesthetics scale mentioned below.)

Some pages of interest for reference/information:

• Rob's Puzzle Page. A ridiculous collection, with references to stores - at some point maybe I'll go through and point out ones that appeal to me.
• Polyhedral Dissection Discussion.
• Design Competition.

I'm also getting somewhat interested in the theory behind these things. For example, there's some interesting discussion of the six-piece burr here (although past the first few pages, most of it starts going over my head). On the other hand, though the discussion is interesting, the puzzles themselves quickly diverge into nightmarish arrangement/sequence puzzles, which is not ideal. But solving and abstractly considering are different things. Thinking about disentanglement puzzles is interesting, too.

• 5-Dimensional Rubik's cube.
• Puzzle.
• NotPron (self-described hardest puzzle on the internet).