I discovered git-annex recently which I find awesome. It was designed for managing large files efficiently. I use it for my photo/music (etc.) collections. The development of git-annex is very active. The content of the files can be removed from the Git repository, only the tree hierarchy is tracked by Git (through symlinks). However, to get the content of the file, a second step is necessary after pulling/pushing, e.g.:
$ git annex add mybigfile
$ git commit -m'add mybigfile'
$ git push myremote
$ git annex copy --to myremote mybigfile ## This command copies the actual content to myremote
$ git annex drop mybigfile ## Remove content from local repo
...
$ git annex get mybigfile ## Retrieve the content
## or to specify the remote from which to get:
$ git annex copy --from myremote mybigfile
There are many commands available, and there is a great documentation on the website. A package is available on Debian.