I think the most influential books on me are those that ask questions that I continue to try to answer, long after finishing the book. I use these works as a kind of touchstone to understand something in my immediate environment that I find troubling or perplexing.

The Aeneid

The Divine Comedy

Don Quixote

Rashomon (which I only know from the Kurosawa film) / The Sound and the Fury

The mysteries of Ross McDonald

Almost anything I've read by Flannery O'Connor

I haven't read that much modern and contemporary fiction; I'd probably include more of these works here (e.g. the novels of Toni Morrison).