You can find free git hosting for public git repositories in a few places.
gitorious.com
Free hosting for seemingly unlimited repositories, organized into projects. It has some social components. Gitorious is also an open source project, so you can deploy it on your own server if you can manage. It is a very large complicated application that is difficult to deploy.
github.com
For the free version, you can have up to 100MB of repositories. It is built around being a social code site.
sourceforge.net
Projects require approval, but hosting is then unlimited. It also provides options for other repositories. Features like web hosting and wikis and bug tracking are also available.
You can also host your git repositories on your own server.
gitosis
Available in the ubuntu repos. Managed by editing a configuration file and committing it to the gitosis-admin repo. The only authentication option is ssh keys.
gitblit
Easy to install, runs on tomcat6. It stores it's data in the git repository, so there is no need for any database engines. The only authentication option is http password authentication.