The first SHA1 collision was announced today, produced by an identical-prefix collision attack.
After looking into it all day, it does not appear to impact git's security immediately, except for targeted attacks against specific projects by very wealthy attackers. But we're well past the time when it seemed ok that git uses SHA1. If this gets improved into a chosen-prefix collision attack, git will start to be rather insecure.
Projects that store binary files in git, that might be worth $100k for an attacker to backdoor should be concerned by the SHA1 collisions. A good example of such a project is <git://git.kernel.org/pub/scm/linux/kernel/git/firmware/linux-firmware.git>.
Using git-annex (with a suitable backend like SHA256) and signed commits together is a good way to secure such repositories.
Update 12:25 am: However, there are some ways to embed SHA1-colliding data in the names of git-annex keys. That makes git-annex with signed commits be no more secure than git with signed commits. I am working to fix git-annex to not use keys that have such problems.