I highly recommend starting with Cat's Cradle over Slaughterhouse Five, especially if you like thinking about religion (and the silliness of religion, dictators, and technology)

UPDATE: Thank you all for the suggestions. I will pick up Cat's Cradle next :)

By the way, the Keys to Great Writing is an awesome book. It has made me critique everything I write, in a good way. I even thought twice before submitting this comment.

UPDATE 2: Fix: Use the verb critique rather than critic (one who does that).

In the spirit of helpfulness, I think you mean "critique". :-)

Yes! Thanks :)

Oh you are in for a treat! Cat's Cradle is a great one to start with, easy to get into and an excellent balance of clever and funny. Mother Night is superb, gripping and profound.

Cat's Cradle is also excellent. Honestly just dive in.

My favorite of his is Mother Night. The moral being: "We are what we pretend to be, so we must be careful about what we pretend to be."

Breakfast of Champions if you want to read something outrageously funny and a little bit sad.

Cat's Craddle is a light and entertaining introduction to Vonnegut's general insanity.

His most famous novel (I think) is Slaughterhouse-Five. I enjoyed it a lot. So it goes.