Attorney General Hillary Clinton? Secretary of State? Justice?
What would Hillary Clinton Want from Obama? Is it the Vice Presidency? Jim might well be right that Obama might have good reason to offer Clinton this, and it might even make for a strong ticket (though I'm not sure that would be so). But I wonder whether Hillary would want this. The Vice Presidency is a notoriously low-power job. A President who genuinely trusts the Vice President may bring the Vice President informally into lots of important decisions (consider Bush and Cheney), but I doubt that Obama would be willing to do this with Clinton, or that Clinton would much like this sort of role.
The Vice Presidency is often a stepping-stone to the Presidency, but I doubt that it would be for Hillary, who'll be 69 in November 2016 — quite old for a first-term President, notwithstanding Reagan and McCain. Query how the higher life expectancy for women plays out here; query also how the conventional wisdom that men are seen as aging more gracefully than women (I stress "seen" here, because that's the relevant matter) might come into play. But I do suspect that she won't see herself as a viable 2016 candidate, and a 2012 insurgent run against a President Obama would likely be impossible if she's part of the Administration.
Nor would running as Vice-President and losing increase her chances of being the Presidential nominee in 2012; if anything, it would likely decrease them. Maybe she might just like the historic element of being the first female Vice President, but I doubt it.
What then might Clinton want more than her job as Senator? How about Attorney General or Secretary of State? Would it look bad for Obama to make this sort of offer before the election? (My sense is that primary rivals do sometimes get Cabinet positions, consider Bush Sr. and Jack Kemp, but that no deal is generally made beforehand.) How about Supreme Court Justice, for which there is something of a precedent in the Eisenhower-Warren situation, though I understand that it's not clear whether there had been an explicit deal?
Would she want those sorts of positions? Would she be an asset to the campaign if such a deal were announced beforehand? What if no such official deal were announced, but a quiet offer and acceptance led her to withdraw, publicly endorse Obama, and enthusiastically campaign for him?
This is way outside my area of expertise, so it may well be that all these options are nonstarters, and that I'm mistaken about her likely lack of enthusiasm for the Vice Presidency. Still, I thought these might be interesting alternatives to discuss.
UPDATE: Commenter GV, writes "What reason would Obama have to offer Clinton anything? Since Indiana, she has stopped attacking him, so the primary no longer hurts him. She has already said she'll campaign for him if she loses. It's clear to everyone now, even Hillary, that this race is over." I take it that one reason would be to win over some of the Hillary partisans who might otherwise be miffed at how he and his voters have treated their candidate, and who might therefore stay home come election day.