Author Avatar: One gets the sense that he is the main character in many of his own movies. Maybe the most obvious was Edward Scissorhands, whose main character was a messy-haired Eerie Pale-Skinned Brunette with a macabre look about him who had trouble fitting in. This goes double if played by Johnny Depp - one Hollywood producer explained that "Basically, Johnny Depp is playing Tim Burton in all his movies." Depp actually agreed.
Circus of Fear: Elements thereof crop up in Pee-Wee's Big Adventure, Beetlejuice, both of the Batman films he directed, The Nightmare Before Christmas, and Mars Attacks!, among others. Subverted in Big Fish, whose circus people are genuinely friendly folks (although the ringmaster is a werewolf).
Creator Backlash: Not as extreme as some examples, but he once confessed that, with the exception of Pee-Wee's Big Adventure, he doesn't much enjoy watching his older films because the memories are too personal for him to view them objectively.
Creator Thumbprint: As listed at the trope entry, there's unusual hands, German Expressionism, dogs, Goth Spirals, and stripes. To a lesser extent, snowy settings, especially if Christmas is involved. Above all these, he loves protagonists who are outcasts in some way.
He also seems to like casting his attractive girlfriends alongside much hotter male leads. He also seems to like killing off (Mars Attacks! (shot), Sleepy Hollow (iron maiden), Sweeney Todd (roasted alive)) or at least giving a less-than happy ending to said girlfriends (Big Fish (spinster cat lady), Alice in Wonderland (exiled), Dark Shadows (seemingly killed and dumped in the ocean, but survived) and Planet Of The Apes (then-girlfriend Lisa Marie and future-wife Helena Bonham-Carter were implied to be erased from history).
Dark Is Not Evil: It can be benign, world-weary, friendly, helpful — even lovable. That said, when dark is evil, or at least angry, watch out.
Deliberately Monochrome: Ed Wood and Frankenweenie are in outright black and white, Halloween Town in The Nightmare Before Christmas only has touches of color, Sweeney Todd is shot in mostly desaturated colors, and the living world in Corpse Bride is much grayer than the world of the dead.
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 no more than inspiring the artistic style.
Our Monsters Are Different: Many of Burton's protagonists consist of characters who are viewed as terrifying to other characters, but they're actually the heroes of the piece, even if what they do is not in tune with everyone else.
Person as Verb: "Burtonesque" is often used to describe something with a gothic, quirky style.
Playing Against Type: While Burton's choice to cast Michael Keaton as Batman was surprising at the time (see trope entry), it's his work with Johnny Depp that's most famous for invoking this trope. Depp was eager to move on from 21 Jump Street, which made him famous but threatened to typecast him, and doing Edward Scissorhands (and, for John Waters, Cry-Baby) in 1990 was incredibly effective. "Eccentric protagonist" has become Depp's "type" for Burton.
Recycled Trailer Music: The scores for Pee-Wee's Big Adventure, Edward Scissorhands and The Nightmare Before Christmas turn up as the music to trailers for other films quite often.
Scenery Porn: It's not for nothing Batman, Sleepy Hollow, and Sweeney Todd won art direction Oscars.
Retraux: Many of his films are made to look as if they're set during the forties, fifties, or sixties (the years of Burton's childhood and his parents' adolescence), with contemporary elements seeded throughout.