Expanding on Noufal Ibrahim's answer, use the --short flag with git-symbolic-ref, no need to fuss with sed.
I've been using something like this in hooks and it works well:
#!/bin/bash
branch=$(git symbolic-ref --short HEAD)
echo
echo "**** Running post-commit hook from branch $branch"
echo
That outputs "**** Running post-commit hook from branch master"
Note that git-symbolic-ref only works if you're in a repository. Luckily .git/HEAD, as a leftover from Git's early days, contains the same symbolic ref. If you want to get the active branch of several git repositories, without traversing directories, you could use a bash one-liner like this:
for repo in */.git; do branch=$(cat $repo/HEAD); echo ${repo%/.git} : ${branch##*/}; done
Which outputs something like:
repo1 : master
repo2 : dev
repo3 : issue12
If you want to go further, the full ref contained in .git/HEAD is also a relative path to a file containing the SHA-1 hash of the branch's last commit.