The big one for Git is Overcommit[1]. The tools that it runs depend on the language, though. Some are community-driven[2], while others are baked into the language.[3]

[1]: https://github.com/brigade/overcommit

[2]: E.g., flake8 for Python: https://pypi.python.org/pypi/flake8

[3]: E.g., gofmt for Go: https://golang.org/cmd/gofmt/