You have also
git symbolic-ref HEAD which displays the full refspec.
To show only the branch name in Git v1.8 and later (thank's to Greg for pointing that out):
git symbolic-ref --short HEAD
On Git v1.7+ you can also do:
git rev-parse --abbrev-ref HEAD
Both should give the same branch name if you're on a branch. If you're on a detached head answers differ.
On an earlier client, this seems to work:
git symbolic-ref HEAD | sed -e "s/^refs\/heads\///"
– Darien 26. Mar 2014