You can scour listings for jobs and apartments, lowball people trying to get rid of some of their stuff or see if anyone thinks you're their missed connection wherever you are, without having to use Craigslist's mobile site. On the flip side, you can also use the free app to post and edit classified ads fairly easily.
There have been other Craiglist apps for iOS and Android over the years, including officially licensed ones. Craigslist's Android app isn't formally available yet, but can try a beta version of it.