git clone --single-branch --branch <branchname> <remote-repo>
--single-branch option is valid from version 1.7.10 and later.
Please see also the other answer which many people prefer.
You may also want to make sure you understand the difference. And the difference is: by invoking
git clone --branch <branchname> url you're fetching all the branches and checking out one. That may, for instance, mean that your repository has a 5kB documentation or wiki branch and 5GB data branch. And whenever you want to edit your frontpage, you may end up cloning 5GB of data.
Again, that is not to say
git clone --branch is not the way to accomplish that, it's just that it's not always what you want to accomplish, when you're asking about cloning a specific branch.