I\'m using dropbox for random text notes (org-mode) and dot files that I bootstrap, namely
You can use dropbox, just not for a full bare Git repo (because of the high number of files to synchronize and the risk for a corrupted repo if even one of those file doesn't get sync properly, as shown in "Git ref master now empty, how to recover?").
I prefer to use dropbox in conjunction with a git repo bundle (ie one file):
See "Git with Dropbox" and "Backup a Local Git Repository".
See a detailed analysis in this blog post.
You can see an example of a script for that kind of task here (example by shtirlic (Serg Podtynnyi)):
#!/usr/bin/env ruby
if __FILE__ == $0
bundle_name = ARGV[0] if (ARGV[0])
bundle_name = `pwd`.split('/').last.chomp if bundle_name.nil?
bundle_name += ".git.bundle"
puts "Backing up to bundle #{bundle_name}"
`git bundle create ~/Dropbox/backup/git-repos/#{bundle_name} --all`
end