I think a lot of the comments here are good - but a thing to keep in mind with github is that their free repo hosting is by default - public. Which means that your code is indexed and searchable - by anyone visiting github including anonymous users. They do give you free private repos if you are a college student or professor.
I am a big advocate of self hosting - not because services like github suck (in fact I'm a big fan of github, bitbucket and other services) but you have more control over your own code (that and you can setup private repos).
Here is a small list of self hosted solutions (I forked indefero into srchub - many don't like the google code feel but I personally like it for the simplicity and the fact I can easily fix/modify/add on to it):
http://softwarerecs.stackexchange.com/questions/3506/self-ho...
I think it should also be noted that if you're using Heroku, you've already got a "private git host" right there. People get so used to "git push heroku master" as an idiom that it doesn't occur to them that "git pull heroku" works too. You can collaborate using Heroku as a single-source-of-truth just as well as you can using Github or Bitbucket.
tl;dr; free services are fine - just make sure you have backups of all your data
For most individual projects - they are probably good enough. However, the thing to keep in mind is that for free they usually limit features (I think bitbucket limits the number of developers) or remove features all together (google code removing downloads support, github did at one time but reintroduced it). I'm not saying that I think they should be offering everything for free and shouldn't take away features - they have to make money - but in my opinion always have backups and a plan B in case you need to jump ship.
I was a huge google code fan (the design isn't Web 2.0 with social integrations - but I prefer functional over design) until they pulled the plug on downloads support (which for most Linux people isn't a big problem - a make && make install and it's compiled AND installed - for Windows it's not that easy). Which forced me to self host - I do mirror many of my public projects on github but in the event github management decides to remove/reduce a feature I won't be struggling to find a new "home" for my ~100+ projects.
Also - if you look at the issue tracker for google code it's pretty obvious that Google is no longer supporting or even monitoring it (several spam issues have been appearing). I don't have a crystal ball - but my best guess is that Google will pull the plug on Google Code as well. And it would make sense - most people have already "fled" Google Code for github/bitbucket etc.
With that said - let me put on my tin foil hat and say that even if we ignore any potential future issues there could be potential privacy issues if you upload your code to a private repo hosted by someone else. I'm personally not the type to snoop, but that might not stop some lowly intern from getting curious. Or even some bug on their site that makes private repos public (for a short time anyways). Did you hear about the time that Dropbox made passwords optional for four hours [1]?
I am a big advocate of self hosting - not because services like github suck (in fact I'm a big fan of github, bitbucket and other services) but you have more control over your own code (that and you can setup private repos).
Here is a small list of self hosted solutions (I forked indefero into srchub - many don't like the google code feel but I personally like it for the simplicity and the fact I can easily fix/modify/add on to it): http://softwarerecs.stackexchange.com/questions/3506/self-ho...