Amazon themselves don't provide a way to run your own EC2, but Eucalyptus [1] is an open-source implementation that works for some use-cases. I believe OpenStack and CloudStack also implement a good portion of the AWS APIs.
Last I checked, Eucalyptus is missing an number of the APIs that customers really use once they are doing more than just hosting a few VMs. Access control, security, VPN... The service providers are actually quite different and any attempt to standardize is just doing to be the least-common-denominator, which is going to be missing a great number of useful features.
