With gitosis, is it possible to specify write permissions so that users can push freely to branches with their own name, but not merge with the master? E.g. $USER/test1 .. $USER/test5
This mean you could host just one repository per project, rather than hosting multiple repositories for the same project, specific to each user:
project1-user1
project1-user2
project1-user3
...
project5-user1
project5-user2
project5-user3
Gitosis controls access to repositories, but not by branch or commit. So you could put the master in a repo by itself which had read-only access and let users push their individual branches to another repo ( or one per user, as you say). I haven't seen anyone extend gitosis for finer-grain control.
If you really need to restrict your users' access that much and you want to use Git, then perhaps you should only take patches by e-mail and keep your repo as read-only.
This script[1] seems to do per branch access control http://www.kernel.org/pub/software/scm/git/docs/howto/update-hook-example.txt
The Gitolite project offers this functionality. It's a rewrite of Gitosis in Perl. Its code can be found on github
When I first wrote this answer, it didn't support gitweb or git-daemon integration, but it does now.