Now that we have the hints, my best guesses are Gore or Clark, with Bloomberg a very long shot.  I invite others to weigh in with the following criteria in mind. Overall I think the choice will clearly send the message that this will not be a politics as usual and that he intends for his VP to have a very substantive executive role--not the bucket of warm spit but an overtly executive function (this can't be confused with Cheney as brains and puppeteer). Obama says, "independent" and someone who will challenge his thinking. To me that is someone who is not currently holding office (Bloomberg can be excepted here because he is under term limits).  Independent can also mean hyper wealthy but also self-made, again Bloomberg can do that. At the same time it has to be someone who is very well-known and widely respected, especially by the MSM.  I think Obama is someone who does not need the spotlight all the time and will pick someone who can challenge him, and also tease him and make him laugh at himself. That's what "independent"means. (Sorry Hillary lovers, as a pair Obama and Clinton are not wired for that kind of chemistry.)  Imagine Obama getting ribbed by his veep.  I think that would make everyone relax a bit.  And McCain seems completely unable to laugh at himself--his humor is of the flyboy, wink, wink, nudge, nudge variety. 
I realize Clark doesn't meet all the qualifications but dammit he was spot on about McCain's riding his non-executive level military experience as a qualification for the presidency and he has been relentless in his work on behalf of the Dems and of Hillary.
I think Al would do it--he is senior statesman and great fun to be around these days.

You've got to take Michele into account--she has got to like the guy/gal and spouse a lot. And just to to remind folks, Tipper and Gertrude are both terrifically smart and personable. Bloomberg doesn't believe in marriage so I guess you can leave him out on that one.  Let's hear what you think.