Is it possible? I want to create a small community site, but do not want to use a Live ID.
Sharepoint has an extensible authentication provider model, so you can use it to expand to support openid.
See the OpenID Membership Provider Project on CodePlex. This provides OpenID support for SharePoint.
If you are looking for a Windows-based community site infrastructure, I would suggest Community Server, which has a free license and native OpenID support.
http://communityserver.com/products/express/
Many have already done this with DotNetOpenId with SharePoint.
There are some discussions on the dotnetopenid mailing list that cover this topic. Feel free to post your question there to get answers from the few people who have done this.
There are two solutions that exactly match your requirements: SharePoint requirements provider for authentication based on SharePoint requirements using the Windows Live ID and another OpenID provider such as Google and Yahoo. it will allow you and your members to access your SharePoint site with any OpenID or Windows Live ID provider.
SharePoint Live Authentication: http://www.shetabtech.com/english/SharePointLiveAuth