I've done a lot of research on this, and the Nokia Asha 501 is the best dumb phone I've found: http://amzn.to/1HncbcC
I purchased it because it was the most smartphone-like phone on which AT&T does not require a data plan (my definition of dumb phone, yours may vary). The battery lasts a few days when using it mostly for music and internet, or a couple weeks (!) when using it for calls only. It's small, but not too small to be useful. With it's built-in WiFi, it's the only dumbphone that I know that will do Facebook, Youtube, Twitter, Email, and even a small number of games.
This is not going to touch any iPhone or Android phone by a long shot, but for the price it does pretty well.