Django is incredible - I wish I'd started with it. It's truly the most useful framework I've ever used - a real workhorse for building applications.
Flask and bottle are minimalist and get the job done for focused tasks - for example I hacked together various web examples into an mjpeg server recently used Flask (based on Miguel Grinberg's webcam server). You can get a simple web site up and running in 3 minutes with bottle or Flask. I'd recommend against using them for anything bigger though - you'll just spend all your time reinventing Django (badly).
I use Sanic for asynchronous web servers.
Falcon is great to use to build APIs - it's raw and minimal and built to task.
Indeed in my latest project I use Django for the main web application, Flask for the mjpeg server and sanic as a long polling web server acting as a message queue server.