You've reached the OpenID server of Isaac Z. Schlueter.
My OpenID url is: http://foohack.com. So, if you see anything on the internet signed with that URL, you can blame me for it.
OpenID is the future of identity on the internet. It addresses a central--if limited--aspect of the the biggest deficiency in internet technology today. Check out OpenID.net for more information on OpenIDs.
Owning your identity provider is a key part of doing identity properly. If you don't own your identity provider, then you don't really own your identity, and we're back to the bad old days of having some (possibly untrustworthy or unreliable) institution that must validate your existence.
At best, you are bound to their policies and limitations; at worst, they violate your trust and you're boned. Furthermore, some may be more shady than others. Therefor, rather than actually provide a way for you to prove that you are who you say you are, the third-party system only complicates the process by forcing us all to manage two sets of trusts: one for people we trust, and another for those we trust to tell us who to trust.
At some point, I may write up something on running your own OpenID server (it's not quite trivial) or even attempt to bundle this up into an easy to install package. It'll be on my blog if I do so.
For now, if you're interested, I highly recommend using either Yahoo! or one of the other many OpenID providers out there. (Chances are, you already have an account with LiveJournal, LinkedIn, Plaxo, Flickr, or someone else.) While it's not ideal, having your identity served from a single online account you somewhat control is still quite a bit better than creating a new identity everywhere you go.
No.
The whole point is for you to host it on your OWN domain. If you can't do that (or don't want to go through the trouble of setting it up) then you should use an identity provider that has a large infrastructure for managing user data, a very good user-centered privacy policy (including strict rules for account deletion), and a history of trustworthy behavior on behalf of its users.
Also, it should be an identity that you're already associated with, so that you don't have to re-associate yourself with a new identity, and it ought to support the most current OpenID standard.
Excepting the occasional Chinese democracy advocate, Yahoo! has a very good track record of strict user-centric behavior, a very strong privacy policy, very straightforward and powerful account-deletion policies, and as of today support OpenID 2 exclusively. Chances are, if you've been on the internet for any length of time, you have a Yahoo ID already. Even better, you don't have to remember or type your full OpenID URL--just typing "yahoo.com" (or clicking "Sign in with Yahoo") is enough.
If you don't like Yahoo!, there are lots of other sites providing OpenID URLs for their users.
I'm somewhat opposed to the practice of delegated identity validation, and I'm certainly not about to get into the business of vouching for people's identities.
Keep an eye on the chi.mp project. On September 1, 2008, you'll be able to register a .mp domain for your own identification purposes, free of charge.