Olympus Stylus Epic is another designation of Olympus µ-II mentioned in other posts above.
+1 for the little rollei 35. I used a 35B for many years as my only camera - lowest spec lens in the range. Nothing wrong with the images it took - certainly up there with any other compact camera. used on middling stops the DOF is huge (e.g. DOF markers show 6ft to inf at F16) and the fact its a view camera and not a rangefinder is hardly a problem in normal use.
Not the fastest camera to use because you always have to extend the lens, and don't forget to use it upside down if using the bottom mounted flash if you don't want people to have dark halo's!
Many of the cameras mentioned do take great photos but some are getting expensive. I keep an eye open for them but they just don't find their way into the Thrift Stores I shop in. I manage to find this Konica A4 on the bay for $17. After running a film through it I can recommend it. It is sleek and small enough to put in your shirt pocket.
Konica A4 P&S by dbuckle2695, on Flickr
Open by dbuckle2695, on Flickr
http://tomchuk.com/misc/rf/ It's astounding precise. You can stick it to the back of the camera. Besides: The lens is only 40mm. If you don't try to make macros you will get away with hyperfocal focussing most of the time.
ED: Just seen that Heinz had posted the same link a while back. But as an add on:
one of the pros of the little Rollei is, that you can make all the necessary dial ins without taking the camera to the eye. Then you raise the cam to the eye and take your picture within the blink of an eye. It's priceless for snapshots.
+1 for the XA
I'm surprised no one has mentioned the Minox 35GT: legendary for an autoexposure system that gets reciprocity failure right.