I've dabbled with Sinatra, but haven't really written anything serious with it.
As you said above, there's a list at http://www.sinatrarb.com/wild.html, although a lot of the applications listed there seem to link to GitHub pages, which I assume are often people experimenting with Sinatra and publishing their results online. Then, there's also the Sinatra mailing list, where you might find links to some interesting projects.[*]
As for your question on when to use Sinatra, I personally would answer "for smaller projects." When you want something up and running very quickly, it seems like Sinatra is an excellent choice. It's also great for people who like Ruby. With that I mean, when you're doing something in Rails, you have to do it "The Rails Way". Rails is the framework upon which you're building your application, and you have to adhere to its customs and conventions. Sinatra, on the other hand, feels like a library. You feel like you're writing Ruby, if you want to connect to a database, you use the library you like/think is appropriate for the job, if you want to output HTML you choose the templating library you like, and if you want a simple web framework, you choose Sinatra. Sinatra is not something upon which you build your whole application, it's something you use beside the rest of your application.
So, as you may have gathered, I'm quite fond of Sinatra, and I would use it for personal (or small-scale) projects. It's easy to set up and easy to use, as long as you know what you're doing. Looking through http://www.sinatrarb.com/wild.html, it seems like that's what most people are using it for, see for example Is Lost on yet? and Calendar About Nothing.
[*] Edit: I found a thread here, with people linking to their projects. There seem both larger and smaller projects. Very interesting stuff.