The Bitcoin.org domain was registered on August 18, 2008 -- presumably by Satoshi Nakamoto before even publishing the Bitcoin design paper. (Note: the Bitcoin.org site says it was co-registered by Sirius, although Sirius says he wasn't involved in Bitcoin until 2009.)
The Bitcoin.org site was hosted on Pages.GitHub.com from 2011 to 2014. It was moved to an independent server in early 2014 for the Bitcoin Core 0.9.0 release so that the Bitcoin Core binaries didn't have to be hosted on SourceForge any longer. Funding for the server came from the Bitcoin Foundation and has been continued through to 31 August 2015.