Award Snub: He's never been nominated for an Oscar as a director. The closest he's come to winning any Oscar was for co-directing Corpse Bride, which was one of the 2005 nominees for Best Animated Feature.
Not to mention Henry Selick, whose stop-motion style is very Burton-esque; so much so that Burton produced two of the films he directed (James and the Giant Peach and The Nightmare Before Christmas). (It also caused some people to assume that Tim Burton was involved with Coraline, when in reality, his involvement was probably inspiring the artistic style)
Hate Dumb: These movies suck merely because of the fans who like them, and because I've seen *Insert movie here*'s products at Hot Topic!
Hype Backlash: Few directors are as blatant and consistent with their Signature Style and Author Appeal, so if his aesthetic isn't what you're looking for, you will experience this -- especially with the films that are adaptations. The heavy merchandising his films have gained over the years doesn't help, nor does his association with the Goth and Emo Teen subcultures.
The Hype Backlash is so bad, there are people saying that they won't even see the movies merely because it's being marketed at Hot Topic.
You just know this is going to double back into that other trope one of these days.
Nightmare Fuel: Most of his movies have it in varying degrees (see the Film and Western Animation examples). Batman Returns got in outright trouble for it with parents partly due to Misaimed Marketing (see that trope's entry).
Scapegoat Creator: Being a director, almost all of the movies he directed were apparently produced, directed, written, created, etc by only one person: Tim Burton. The only thing he apparently didn't do for the movies was act in them. The most recent backlash was about the recent Alice in Wonderland, which was apparently written by him despite that even looking at the credits or its page on The Other Wiki can tell you otherwise.
Tear Jerker: Edward Scissorhands, Big Fish, Corpse Bride, Sweeney Todd.
For many fans, the most notable example is Ed Wood. More specifically, Bela Lugosi towards the end. Martin Landau's performance got the Oscar it deserved.
Ugly Cute: Most of his characters, as well as he himself.