Ive been thinking about writing this for a while and a recent entry spurred me to finally do it.  Each candidate has specific requirements that they will need in their VP choice, and therefore some people who are options with one of the candidates, won't be with one of the others.

Clinton
Needs: Clinton has more options available to her than either Obama or Edwards.  She will not pick a woman, but other than that can pick any male she wishes.  If the race comes down to Clinton v. Obama, and Clinton wins, she will be much more likely to pick a minority.  The biggest key for her is someone who is viewed as an outsider, and not from Washington.
Possible Picks: I doubt that Obama would take it, but Clinton is the only one who could pick him, Edwards would never pick Obama as Ill explain later.  However, if it comes down to her and Obama Clinton will be much more likely to pick a minority.  That is why you shouldn't be surprised if you see Harold Ford on the ticket as he could easily be picked by Clinton.  Other top possibilities are Bill Richardson, Mark Warner, Evan Bayh and Wes Clark.