The Caves of Steel by Isaac Asimov - A classic, deservedly so; I love the homoerotic undertones of R. Daneel Olivaw's relationship with Lije Bailey (whom he insists on addressing as "partner Elijah").
The Martian Chronicles by Ray Bradbury - Ditto, of course. This book is a literary masterpiece. I love the symmetry of the structure, and the variations on the "house of mirrors" theme. Particularly haunting is the way the Humans and the Martians never directly interact in the book; they are literally living on the same planet but in different worlds.
National Velvet by Enid Bagnold - This is about so much more than a girl riding a horse. It really is all about gender. I couldn't help thinking that the race was, for Velvet, as much a pretext to "pass" as a boy as anything else. The minor characters are vivid and arresting. Lots of undertones around gender and sexuality here.