Q: Do you know of any writers who have gotten at least
two novels published without the aid of an agent, excluding vanity
presses—only small press through university through NY press?
A: The first author who comes to mind is Steve Almond, thought he doesn't strictly fit your description. He published three books, including the nonfiction work Candyfreak (Algonquin) and the short-story collection My Life in Heavy Metal (Grove Atlantic), without the benefit of an agent. You can read some of his success story right here at Identity Theory, in a Robert Birnbaum interview.
Almond wrote a piece for Poets & Writers in early 2004, "Are Agents Necessary?" He has made this piece available on his home site. (You can read some of the feedback to his article here: http://www.pw.org/mag/0403/letters.htm.) At the time, he wished for a world in which authors and editors could work together in harmony without the interference of an agent. He said, "Fellow writers almost always assume that I don't have an agent because I can't find one. ... I then have to explain that I don't have an agent because I don't want one, which causes them even more confusion."
I noticed, however, in April 2006 via PublishersMarketplace.com, that Almond's most recent work was sold by agent Jeff Kellogg. I don't know if Almond has changed his mind about agents, but it does seem to mark a departure from his earlier philosophy.
I'm sure there are more examples of authors who sold their first two novels without an agent. If any readers know of a good example or a good story, write me at editorfriedman (at) mac (dot) com.