According to DNS Lookup wwww.bitcoin.org is (today) just another another name for vhost.sourceforge.net so it is run by the sourceforge guys. As the DNS Authority for the www subdomain is bitcoin.org you might be interested in that as well.
According to WHOIS bitcoin.org is run by:
Domain ID:D153621148-LROR
Domain Name:BITCOIN.ORG
Created On:18-Aug-2008 13:19:55 UTC
Last Updated On:18-May-2011 04:47:13 UTC
Expiration Date:18-Aug-2019 13:19:55 UTC
Sponsoring Registrar:eNom, Inc. (R39-LROR)
Status:OK
Registrant ID:02e87e389a273cab
Registrant Name:Louhi Net Oy
Registrant Organization:Louhi Net Oy
Registrant City:Helsinki
Registrant Country:FI
Registrant Email:hostmaster@XXXXXXXX
Admin ID:02e87e389a273cab
Admin Name:Louhi Net Oy
Admin Organization:Louhi Net Oy
Admin City:Helsinki
Admin State/Province:
Admin Country:FI
Admin Email:hostmaster@XXXXXXXX
Tech ID:02e87e389a273cab
Tech Name:Louhi Net Oy
Tech Organization:Louhi Net Oy
Tech City:Helsinki
Tech Email:hostmaster@XXXXXXXX
Name Server:DNS1.LOUHI.NET
Name Server:DNS2.LOUHI.NET
Name Server:DNS3.LOUHI.NET
DNSSEC:Unsigned
Although it does not look very trustworthy this is a common hosting setup. It may differ from NIC to NIC but usually the real "owner" or his responsible person is mentioned as Admin.
It's my understanding that bitcointalk.org has been switched to a new arrangement after the recent hack. – eMansipater – 2011-09-14T01:53:19.363
1Well, Mark (of MtGox) took over the hosting I believe. Martti still owns the domain. I will update my answer once I've looked it up more carefully. – D.H. - bitcoin.se – 2011-09-14T05:12:39.240
2Sirius continues to have exclusive control over the DNS for both sites, though hosting is now handled by other people. – theymos – 2011-09-25T18:58:35.690