Big fan of crosswords, particularly the Sunday NYT and the Washington Post Sunday one (I can't recall who does that, it's also carried in other papers). I tend to do them back to back, so my personal pet peeve is when they repeat clues between the two puzzles, sometimes on the same day's puzzles!
Sudoku, both samarai and original flavors. Not as big a fan of the 4x4 blocks, the ones that use letters, though.
Anagrams/jumbles, especially the Scrabble (game) one. I've occasionally done the cryptics but our current paper doesn't have a good one. Never heard of cryptic crosswords, that sounds really challenging!
Actual jigsaw puzzles. DH's extended family are big fans too, so I brought some of my favorites to share over the holidays. Two of them weren't even considered due to perceived difficulty, and after I left they finally gave up on the one we started because I wasn't there to keep hacking away at it. And I didn't even bring the one that doesn't have edge pieces ("Impossible" puzzle type).