I'll ask the obvious question: how does it compare to Rails? What kind of apps is Sinatra better suited for, and for which ones should I use Rails instead?
Sinatra is much more lightweight.
You need full-blown framework: Rails
You need basic features and minimal footprint: Sinatra
Sinatra is great, by the way.
It's also easy to pull in other libraries that you'd like without the Rails stack making your decisions. At my job, I used it for a simple proof-of-concept ad server that only used ActiveRecord, Thinking Sphinx, Paperclip, HAML, and Treetop. All it does is listen for PUTs from the ad database, parse/store/index them, and then offer up a minimal parameter-based view.
Not to mention that you can put a Sinatra app inside a rails app by sticking it in /lib
one of the speakers at rubyconfindia put it well: when developing your app, use sinatra, because it's a joy to work with. when moving into production, start migrating to rails, because you'll need to add a lot of functionality that rails will have plugins available for.