Slaughterhouse Five is key. Breakfast of Champions is hella proper tight to. There's a huge gap between his earlier fiction and the stuff that began to appear after Slaughterhouse Five, where his style became a lot more lucid.
My favorite book of his (and the one he considers his least favorite) is Slapstick. I think it's well worth a read. Hocus Pocus is also pretty fantastic.
If you want to get a more comprehensive look at Vonnegut, definitely check out Welcome to the Monkey House, a collection of his short fic, and then go grab one of his collected speeches and essays--Palm Sunday is a great read, and an awesome insight into Vonnegut's personal life and politics (if his novels aren't enough).
If you're interested in that, you might want to check out his last book, Man Without a Country, just to see where Vonnegut ended up, about a year or so before he died. I fucking love that guy so much.