I use the Olympus OM-D E-M5. I chose it because I like the retro look and it can easily connect to a variety of old lenses. My favorite lenses are the Pentax Super Takumar 55mm and the lenses made for the old Pentax Auto-110. The former are very popular in vintage lens communities and the latter are the smallest exchangeable lenses ever made for a film camera. I think they're all very fun to use.
Image credit to Kreuzschnabel on Wikimedia
Image credit to Tutu and Ganggang on flickr
Image credit to Howard Stanbury on flickr