I'm trying to get used to it with a simple Google Gadget project. However, it seems OK for me to use in full (ie both in Front and Backend). However, with a simple search, I couldn't see any solid application running entirely on it.
If your requirements fit within what Sinatra can provide, you shouldn't hesitate using it. It's a very straightforward framework and works well. If your requirements are more complex, look at Rails or Padrino, the latter of which is built on top of Sinatra and is actually pretty awesome.