I'm a Bit Bucket user and there are a ton of Github users out there. Git integration would be awesome!
Like (S)FTP(S) support, dedicated applications usually do a better job. SourceTree (made by the Bitbucket folks) is amazing (staging sub-file chunks is great!) and even the GitHub application is pretty spiffy. Limited integration, like some way of seeing if a file is 'dirty', OTOH, would be a nice reminder.
(If you spend time in a terminal, you can also get some nice shell integration for watching the status of whatever repo your CWD is contained within.)
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