I highly recommend the Casio Exilim. It's about and inch thick and I carry it in my pocket alot. Almost too much. I have to remember sometimes that I have it and not to put it in the laundry!!!
Linky:
http://www.exilim.casio.com/
Mine is a EX-Z4U, I bought it about 6 months ago. Right before the newer models came out. I paid about $329 at Radio Shack. Great camera.