This book is similar to the Hitchhiker's Guide series in construction, and nearly as good, but hardly anyone has heard of it. If you're an HHTG fan who's still in withdrawal following Douglas Adams's untimely departure, consider reading some Sheckley.
Mindswap and the short story collections are equally brilliant.
Dimension of Miracles contains a brilliant and haunting idea which I often think about. The hero, Thomas Carmody, has been taken from Earth to receive a Prize in the Galactic Sweepstakes. Unfortunately, there's a catch: the rules of the competition don't provide for a return ticket. He has to find his own way back.
It turns out to be harder than he thought. First, there's the comparatively trivial problem of Where, which involves travelling a few tens of thousands of light-years. Once he's located his home planet, he's faced with When, since he also needs to find the right moment in history (he initially lands some time in the late Cretaceous). But the last question, Which, is the hardest one. Of all the many alternate parallel Earths, how can he recognise his own home? And all along, he's being pursued by a fiendish and inexorable enemy, the Predator.
After many adventures, Carmody does finally solve Where, When and Which and returns to the world he came from. But he doesn't like it, and leaves again. He is now doomed to a terrifying existence where he will for ever have to flee the Predator through increasingly unlikely Earths. His companion, the Prize, asks him what he thinks he will do with his life.
"I will live it," replies Carmody.