git clone -b branchname --depth 1 git@git.example.com:repository.git /path/to/your/repo
This will create a so called "shallow clone". It only contains the very latest commit of the named branch. Thus you will only pull the absolutely necessary bits.
To cite from the git clone
man page:
--depth <depth>
Create a shallow clone with a history truncated to the specified number
of revisions. A shallow repository has a number of limitations (you cannot clone
or fetch from it, nor push from nor into it), but is adequate if you are only
interested in the recent history of a large project with a long history, and would
want to send in fixes as patches.
Edit: AFAIK git can not "export" from a remote directory directly. But the approach above is roughly equivalent to an export from remote. If you then don't want the .git
directory, just remove it. This is way easier than in the SVN world as you have exactly one, not one in every freaking directory.