What aspect of a site's SSL certificate causes IE's address bar to turn green?
I'm working on a site which already uses SSL successfully, but am interested to know if there are different levels of certificate.
Yes, it is a different level of certificate, as you say.
It's green when it is an Extended Validation Certificate. See Extended Validation Certificate at Wikipedia: "[...] a special type of X.509 certificate which requires more extensive investigation of the requesting entity by the Certificate Authority before being issued. [...]"
The cheapest of certificates are usually domain-validation only, meaning the only thing that the certificate authority is guaranteeing is that the requestor of the certificate has control of the domain name. That's a very low threshold. The extended validation certificates require more than that. For instance, they verify the legal status of the business that is requesting the certificate, etc.