I'll just volunteer that BitBucket has worked flawlessly for me for years. Of course I use repos others have setup in Github, but I've never seen any reason to switch.
> Is there anything specifically about GitHub which puts you off, or is it just that BitBucket works so you don't want to change?
The latter + all the hype surrounding the GitHub (thousands of 10-line "Ruby gems" and "JavaScript frameworks" don't help the browsability either). I generally dislike monopolies of ideas/implementations.