Well, "puzzle" is a pretty broad category, so let me narrow it down a bit.
I like many types of puzzle games, but at the moment, there are two particular styles that I'm looking for.
1) Avatar-centric environmental puzzles. These are the game where you control one or more characters and negotiate hazardous environments, typically a series of levels constructed from a set of consistent rules (switches, spike pits, statues that spit fireballs, etc). Some examples are The Lost Vikings, Adventures of Lolo, Deadly Rooms of Death, and Solomon's Key.
Note that I'm not presently looking for the "puzzle platform" games descended from Prince of Persia - Out of This World, Tomb Raider, Ico, Oddworld, Blackthorne, etc. I love those games as well, but they're a little more action-adventurey and a little less puzzly than what I'm looking for at the moment.
2) Abstract object-manipulation puzzles. This is not as specific as #1, but typically this sort of game gives you a playing field with a variety of items or objects to mess with and arrange in order to accomplish some objective or other. Lemmings, World of Goo, Obulis, and The Incredible Machine are good examples. Pipe Dream is a little too simplistic, and borders on the "parlor game" sort of puzzles found in e.g. The Seventh Guest (you want me to complete the knight's tour? Why?). Brickwell and color match games are not what I'm looking for either, nor is Minesweeper.
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I'm looking for challenging puzzles, and I'm OK with twitch requirements. Of the examples I listed above, The Lost Vikings, DROD and Incredible Machine are my favorites (World of Goo was a nice game, yes, but it was way, way too easy).
Trine does come to mind as one that I have yet to play, but I can't see myself playing that one until the price comes down a ways. I only spend $20+ on games that I'm dying to play, and I hear Trine is not much of a challenge.

Defense Grid and Cogs come immediately to mind. Both pretty good. I've been playing a lot of Cogs lately. Indie puzzle games. Avaliable a bunch of different places, quite cheaply.

Braid, maybe? It looks like a platformer but it is very much a puzzle game, and many of them are clever. You only need to ignore the pretentious and clumsy story though.
World of Goo is easy but it's another matter to get the OCD for every level.

I seconded Braid and Cogs.

Puzzle Quest and its sequel?? That's about the extent of my puzzle games...

How about Portal?
That would more or less fall into the first category and is absolutely incredible, if you don't mind short games.

Eets.
A rather charming indie puzzle game.

And Yet It Moves sounds interesting... but i heard it's only ok.
How about Push?
http://www.bonuslevel.org/games/game_push_7.html
(ps... use the mouse)

Braid might be exactly what you're looking for. Cogs is also pretty good (flawless presentation). You might like Chains, too - nice retro physics-based puzzle game. And Trine is pretty cool, even if a bit easy and pricey - when the inevitable sale comes, make sure you get it too.

Hm, maybe Professor Fisswizzle and the sequel Professor Fizzwizzle and the Molten Mystery?
They're both GREAT puzzles, with lots of levels, objects to interact, and downloadable levels.
Also, you could try Rooms: The Main Building. It's pretty unique too.

inb4 weclock: Tetris Attack and Puzzle League!
Crayon Physics is a fun one if you're looking for something more casual/slower. And World of Goo is a really amazing game, I guess it's sort of a puzzler.

Crazy Machines - game is somewhat similiar to TIM series.

Trine has that Lost Vikings kind've gameplay. Here's my review of the game.

Tag is kind of neat, but you may find it a bit on the easy side. It's free though.

THIS.
Also, Obulis.