Favorite (in no particular order):
Anime/Manga: Alien Street, Axis Powers Hetalia, Banana Fish, Naruto, Detective Conan, Natsume Yuujinchou, Petshop of Horrors, Kuroshitsuji, Rurouni Kenshin, Hikaru no Go, Skip Beat, Gokusen, Princess Tutu, Glass Mask, Otoyomegatari, Crystal Dragon, Tokimeki Tonight, They Too Love, Rure, and various Clamp works.
Books: Harry Potter, Good Omens, Howl's Moving Castle, The Solitaire Mystery, The Little Prince, Pride and Prejudice, Matilda
Movies: Amelie, Inception, Toy Story 3, Spirited Away, Moulin Rouge, The Secret Garden (1993), Sound of Music, The Terminal, Red Cliff (Part 1), Rear Window, Pride and Prejudice (2005)
TV Shows: Criminal Minds, Lie to Me, Bones, The Mentalist, BBC Merlin, Supernatural, Project Runway
Fanfiction Cliches: Time-travel, Dimension-hopping, Crossovers, Hidden Identity, Genderbending
Misused Homophones/near Homophones: your/you're, their/there/they're, lose/loose, definitely/defiantly (seriously, WTH). It won't stop me from reading a good fic, but you have no idea how happy it makes me when someone gets it right.
Epiphets: Ravens are birds, and cannot be used to describe a dark-haired character. Blond = male. Blonde = female. There is also nothing wrong with using the character's name.
Super Ukes: Calling them girls with penii is an insult to girls. Most girls aren't that weepy. And they at least have a semblance of a spine. Where did all the backbone go, people?
Character Bashing: Especially if it has no basis in canon. Ron/Hermione/Ginny/Dumbledore betraying Harry for money has NO BASIS in canon.
Gratuitous Japanese: I get that there are some things that cannot be translated; honorifics, when used correctly (there better be a good explanation if Sasuke ever uses 'chan' for Naruto) are welcome. Using 'nani' instead of 'what' is jarring, not clever.
Harem Fics: I don't know...most of the fics I've tried under this label tends to have super-macho men that's just so badass (kind of a jerk) their love interests don't mind sharing him so long as they get a piece of him. Maybe I'm oversensitive but it sounds a bit...sexist? Inverted Harems are no less annoying - all that melodrama, ugh. I have read and enjoyed fics with polygamy, but they tend to be equal from all sides rather than focused on a single character.