If you also would like the camera to have some manual controls such as Shutter Priority and Aperture Priority, look at the Canon A series of cameras A620 and up. The A700 and A710IS have 6X optical zoom.

If you are into ultra thin cameras you will find most of them do not have optical viewfinders and if you have a problem with the LCD in bright sunlight....you may say a few bad words.
Many of the ultra thin cameras produce a soft (not sharp) picture, so be careful which one you choose.

For a real bargain, check out the Sony W30. You can find it for about $199. Thin, Point-and-shoot, and very sharp photos. It does have a viewfinder.

If you want it all....check out the Fujifilm F30.
1.1 inches thick, manual controls, very sharp photos, good low light performance, very strong flash (21 feet).....but alas, no viewfinder. Newegg.com has this for $269 and you get a $50 mail-in rebate from Fujifilm.