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 and directing Frankenweenie, which were nominees for Best Animated Feature at the 2006 and 2013 Academy Awards, respectively.
Creepy Awesome: Pretty much all of his designs and concepts are twisted and strange, yet they have an undeniable charm.
Critical Dissonance: Goes both ways. His highest-grossing movie is the divisive Alice in Wonderland, while his only box office failure (even Big Eyes earned its budget back) was the Acclaimed FlopEd Wood.
Gateway Series: Because he's one of the few hugely financially successful directors in Hollywood to retain a personal aesthetic, his films tend to be where movie buffs first learn to appreciate the people behind-the-scenes.
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. This has gotten so bad, there are people saying that they won't even see the movies merely because it's being marketed at Hot Topic.
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 for more details).
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.