There is chatter out there about Obama picking Hillary as his Secretary of State. It's a fairly shrewd and gutsy move, I think. Obama probably believes that he has to offer her something since he didn't pick her as his running mate, and Secretary of State is powerful position indeed. After all, she could be left in the Senate running counter moves against him if he doesn't do what she thinks he should do.
Consider: She was his last-standing rival for the Democratic nomination. She put 16 million cracks in the ultimate American "glass ceiling." She didn't drop out of the race until she decided to, even though the numbers had been against her for weeks and weeks. If she's in his Cabinet, being part of the executive branch instead of the legislative branch, he can keep better tabs on her. If she remains in the Senate, her power could grow to the level of a senator like Kennedy.
What would be the advantage for Hillary? She would be part of the executive branch instead of the legislative branch. She's still the junior senator from New York, and doesn't have high-ranking seniority on any committees. She would have regular contact with government leaders from other countries. She would have much more influence over Obama by being part of his Cabinet as opposed to just staying in the Senate.
ALSO: Will Obama offer McCain a little something?