There are quite a few wonderful stories about the AIs continuing after humans are gone. "For a Breath I Tarry" by Roger Zelazny, and the whole of the Cyberiad by Stanislaw Lem, are some great ones.

Of course, one of the critical points of "For a Breath I Tarry" is that the machines are just doing what they're programmed to do, maintaining the infrastructure for no one and just sitting in their orbits keeping the power grid going and all, and are actively hostile to any effort to bring the humans back because that would make things complicated and isn't in their programming (since although superficially they can converse and act "intelligently," more so than humans, they can't really grasp the purpose of things.) Also, "With Folded Hands" by Jack Williamson is another perfectly realistic one.