I don't vote, multiple choices needed!
My favorites:
Rocks-gems-dirts-walls: they often cross over with:
Slow and steady puzzles: Coal Mining for example.
Trick levels: they seem difficult, until you find out a small trick that makes them very easy. (example: Happy Twins)
Twin players: controlling two people with the same set of controls? Woot! (I usually attempt to block one of them as soon as I can, and if I can't do that, things get challenging)
I'm partial to two-players puzzles, solely because I can't get used to WADX and Backspace and Enter... gah, too many keys! Why not a simple switch of controls per Tab?
Also partial to monster mazes.
I HATE don't stuff it ups, I stuff em up.
Trickys can be fun, if there's a sufficent clue onto the trick. Can't find such clues on Euler though!