Jakub already mentioned a shallow clone of selected branches is possible, but quite complex to do.
And he added:
Note however that because branches usually share most of their history, the gain from cloning only a subset of branches might be smaller than you think.
I would add that you shouldn't have any VCS tool in a production plateform (you only install/monitor what is necessary for the production to run).
So git archive remains the best way to extract just what you need, as an archive (zip or tar, format that you can then uses without Git, once transferred on the production side)
Update March 2012:
the upcoming git1.7.10 (April 2012) will actually allow you to clone only one branch:
git clone --single-branch
You can see it in t5500-fetch-pack.sh:
test_expect_success 'single branch clone' '
  git clone --single-branch "file://$(pwd)/." singlebranch
'
That feature was then fixes with:
clone --single: limit the fetch refspec to fetched branch
After running "git clone --single", the resulting repository has the usual default "+refs/heads/*:refs/remotes/origin/*" wildcard fetch refspec installed, which means that a subsequent "git fetch" will end up grabbing all the other branches.
Update the fetch refspec to cover only the singly cloned ref instead to correct this.
builtin/clone.c: detect a clone starting at a tag correctly
31b808a (clone --single: limit the fetch refspec to fetched branch, 2012-09-20) tried to see if the given "branch" to follow is actually a tag at the remote repository by checking with "refs/tags/" but it incorrectly used strstr(3); it is actively wrong to treat a "branch" "refs/heads/refs/tags/foo" and use the logic for the "refs/tags/"
  ref hierarchy.
  What the code really wanted to do is to see if it starts with "refs/tags/".
Update Sept 2016: git clone --single-branch --branch tag will work for chained tags in Git 2.11+ (Q4 2016).