Update 2018-05 because this answer still attracts quite some attention. Silex has been discontinued as of January.
There have been talks of getting new maintainers, but as I see it, nothing came of it.
Currently, Slim and Lumen seem like good alternatives, although Symfony v4 can be setup fairly small thanks to the new Flex system.
Silex is probably the one to go currently. It has the best support of modern PHP programming techniques, is developed in sync with its "big" brother Symfony2, unit-tested, well documented and provides possibility to introduce 3rd party libraries through a very good DI-container mechanism.
Personally, I use this framework for anything that does not need extensive caching, user-managing, heavy database interaction or security. So, basically 95% of the web apps I write.