I just got a case that I bought from ebay and this thing si simply the thinnest I've see, it's 0.3mm (according to vendor) and it only cost me $1.18, you can beraly feel it in the phone, and for that price I think its a ggreat deal...
Just got the Best Case (that is the name if the brand) from Target. It is really slim and looks good. There is no carrier branding and it has a nice soft matte finish.
My wife bought me a case called Ringke SLIM. It covers the back and sides. I'm sure it won't protected it from anything other than minor scratches, but I love how thin it feels! I think it was about $10.
If you want thin, it doesn't get any thinner than the Caudabe Veil. According to their website, it's only 0.35mm thin. The case feels flimsy out of the box, but it's held up well after a month of use. The frost looks fantastic on a white iPhone.