A Choice of Gods, by Clifford D. Simak

All but a few hundred humans vanish from the face of the Earth. The remaining few are now almost immortal, and they do well with their robot servants, but without sufficient population they must live without technology. As a result, they develop their latent mental skills, which includes telepathy and interstellar teleportation. Most of the remaining humans go jumping around the galaxy, exploring. Only a few stay behind.

There's some fuss about a strange intelligence located at the center of the galaxy, and there's some to-do about the robots (most of whom have no humans left to serve) building a giant super-computer robot brain to help them figure out the meaning of life or something. Also, it turns out the eight billion missing humans are alive and well on three planets far, far away from Earth. The strange intelligence had transported them there as some kind of experiment. The real experiment seems to be what the robots will do, though. I think (I'm not sure, it was unclear) that the strange intelligence is more interested in the robots than in the development of humanity.

Altogether a disappointing book. I usually like Simak, but not this one.