Well this is a big field but there has to be favourites in here somewhere.

Heres mine.

1. Tetris

2. Hexic HD

3. Bomberman

Funny how the top 2 in my list are from the same guy. Anyways people go for it. :) 

Tetris. Always & Ever.

i agree with that!

Tetris on Gameboy is the best but there are many good ones.

Tetris DS, Tetris 2, Tetris Attack, Picross DS, Puzzle Quest, and likely Boom Blox (will be) are in my 10 ten. I have never played Bomberman but am looking forward to the Wiiware version.

1.) Any form of Tetris Attack. I thought original tetris kinda sucked :x
2.) Portal (definitely made my brain hurt a few times xD )
3.) Echochrome. (some of the scenes really give your brain a wtf. )

i like tetris, and Fire emblem even though its not a puzzle game it reminds me of chess.

Tetris for Gameboy last me a long time. It's one of the few Gameboy games I could pick up today and not feel it has aged at all. Tetris is the single most timeless videogame that has ever been created.

As a backup, the Sudoku in Brain Age has me covered. I also can't wait to pick up Crosswords DS. 

Tetris, no competition.

Also really liked portal, but that has a lot to do with the writing.

Tetris.

Picross DS was pretty good too.

Portal blew my mind.

My favorite endless puzzle games are Tetris, Dr. Mario, sudoku, and Picross.

My favorite puzzle game with a story, beginning, and end is definitely Portal. I really loved Day of the Tentacle too. Right now I'm enjoying Zack and Wiki.