This list will remain relevant until approximately dawn, but as we see the Democratic contest (and, with it, more or less the general up-ticket election) wind to an end (and Clinton’s eternal optimism aside, it’d literally take someone gunning Obama down to prevent his victory now), I’d like to share how I want to see the ticket to look.

Presidential Platform - Primary issues are expanding social programs, funding every educational mandate, expanding access to higher education and progressivizing the tax code, and cutting down on the supply-side/theocratic red tape introduced to the bureaucracy by Bush. Secondary: an effective minimum wage; a strong effort to end the abuse of immigrant labor (legal and illegal); a large cut in pork-barrel spending in the defense sector. Things which should go without saying but which are not really necessarily campaign issues: major investments into and incentives for private development of sustainable growth and energy; an end to the hiring of mercenary contractors; an end to hiring discrimination among translators and other intelligence operatives; some kind of death ray to ward off Italian perfidy.

Oh, and Iraq: The Obama campaign not only needs to end the occupation immediately on winning the Presidency, but in fact should be smuggling individual soldiers out of the country now. Everyone likes a proactive candidate.

Clinton - Clinton’s powerful base of support means that she should play at least some role in the incoming Administration. The problem is that she seems pretty intent on making herself Someone Important - but her entire campaign has been devoted to suggesting that she’s an experienced, forceful national security / foreign policy candidate.

Vice-President would be a mistake - normal VPs are largely ceremonial representatives and the role of the VP on the campaign trail is (a) involuntary, so there are bound to be points scored off the heated primaries; and (b) servile, a sure shot to alienate Clinton’s ferocious supporters among wealthy middle-aged white skags.
While Richardson’s campaign has bent over backwards to emphasize his suitability in that regard (and he was an early Obama supporter), State would seem to be the proper mixture of important and low-profile to fit Clinton into the campaign, and its mandate is indeed national security and foreign relations. Failing that, Defense is a possibility (although it’d be an unorthodox fit); Attorney-General is also a possibility, but it’s also at odds with what I want to see done with the office.

Vice-President - The choice is essentially between Edwards and Richardson; besides those two, it’s anybody’s guess.
Edwards would produce a fairly balanced ticket; while it’s been suggested that ‘elitist’ has been lobbed at both men, it’s worth saying that Edwards struck a nerve of social populism in the South that many assumed to be dead - the media establishment alienates him at its own risk.
On the other hand, Richardson would balance the ticket in a much less conventional but much more meaningful sense: it’d produce a ticket with two ethnic minority members, balanced between the Mideast and Southwest. Richardson on the VP ticket would help offset the Latino community’s generally conservative politics and their strongly favoring Clinton in the primary - and it would provide the Obama campaign with an anchor in the Southwest, something that would help at least somewhat facing that fucking sun-belt lifer.

If the Obama campaign doesn’t use Edwards as VP, it’d seem wise to make him Attorney-General; the office has spent the last two decades being dragged through the mud something horrible, and Edwards has been a consistently trustworthy character in the last two elections. (It’s worth saying, if he was used as VP, that any retrospectives would show him fighting Cheney - and only a McCain/Ahmadinejad ticket would make that look good for the GOP.)  Especially with the unfortunate rise in right-wing survivalists, a basically amiable Attorney General is going to be a must for the next few terms.
As for Richardson - State, probably.

I’ve also suggested that one of the Daily Show people be used as Press Secretary - given that a major prerequisite for the role now seems to be media presence, it’d almost seem fitting to bring a comedian in to do the job. Yes, it’d be terrible seeing progressive idols dragged through the political mud, but really - the office of Press Secretary wasn’t that nasty before Reagan turned the Presidency into a bullshit art.

Miscellaneous - Various other figures could be usefully employed by a Democratic president. Gore should play at least some role in the new administration; Interior would be worth filling with someone visible, and Gore would make a nice fit for the office.

In general, we needed to do this weeks ago - the Democrats need to have a solid base to lay their platform on. It’s worth emphasizing that the Republicans are so dry on ideas they pretty much dredge up interchangeable party flacks to fill vital roles. Just off the top of my head, I’ve filled four cabinet-level positions - and I’ve barely been watching the news.

It’s time to hammer home that the Democrats are the political future of the country, for better or worse. The Republicans have long since abandoned any pretense of loyalty beyond raw, crass avarice; the Democrats are hardly saints, but they occasionally have the desire to do anything that doesn’t involve making the rich richer.