you can use rev-parse for this
git rev-parse --abbrev-ref HEAD
you can also pipe it to pbcopy to put it into your clipboard
git rev-parse --abbrev-ref HEAD | pbcopy
that returns a list of branches, git rev-parse --abrev-ref HEAD returns the name of the current branch, so you can pipe it to another command..
git rev-parse --abrev-ref HEAD
For other folks arriving here from a google search, as of Git 1.8.1 you can do git symbolic-ref --short HEAD to get the current branch name. This may be considered more idiomatic since the docs (https://git-scm.com/docs/git-symbolic-ref) mention using this command for that use case: "Typically you would give HEAD as the <name> argument to see which branch your working tree is on."
git symbolic-ref --short HEAD