His classic stuff's from the 40s. Slan is by far the biggest one - and supposedly written entierly in a single night. So popular that "Slan" has become its own word among science fiction fans, though it hasn't crossed culture barriers like, say, "beam me up" has. Hewrote plenty of other popular novels and short stories, such as The World of Null-A and Voyage of the Space Beagle. He was just about the biggest of the science fiction authors of his period, second perhaps only to Asimov and Heinlein. I believe even then people weren't always too convinced though. I remember seeing a quote from the 40s by Damon Knight, where he said (paraphrasing here) "van Vogt is no giant. He's a pygmy using a giant typewriter."
He kept writing for decades, well into the 80s, and passed away just a few years ago.
edit: hrmm, I'm not doing your homework, I hope.