While the original question is about S3 compatible software for (what it seems) production use, many are interested in the same software, but for local development and testing.
Regarding production-ready solution, there's a great S3 compatible storage software called Riak CS, it's solid and production proven for years, one drawback – it's not simple to setup. There are some limitations, but nothing major that gets in the way, see api / compatibility documentation.
Already a few great answers for development and testing, this will be useful for Docker users – there's docker-riak-cs image that allows to quickly launch Riak CS instance. I've been using it for nearly 2 years for local development and integration testing with great success.
