I’ll just address the Democratic side of the equation.
I’d never heard of Bredesen before, but having read his Wiki page, I agree he’d be a real VP prospect for either Hillary or Barack.
The next President will want to make it clear that his or her VP is not in the Cheney mold, but since Mondale most VPs have had increased access to the President and, to varying degrees, a greater role in their respective administrations than had previously been the case. It just makes good sense for people to know that there’s someone ready to take office if tragedy strikes the White House.
I highly doubt Hillary would ever accept the VP spot from Barack… but no one thought LBJ would, either, JFK, including JFK and Bobby (and LBJ’s ego was even bigger than Hillary’s, and his resentment of JFK as a whippersnapper was even stronger). Who knows what she’d decide until the offer is extended? Anything could happen. Frankly, I doubt Obama would offer it in the first place, given her high negatives and the many other qualified prospective running mates out there (male and female).
I’ll put in a plug, as Saint Cad and others have, for my governor, Ted Strickland. A very popular moderate Dem and former minister (Methodist, I think), fiscally conservative, in the Dem mainstream on all issues. Got his budget passed nearly unanimously by a GOP-dominated General Assembly last year, which is unprecedented in recent Ohio history. I won’t say Ohio is indispensable for a Clinton or Obama win, but it’d sure be nice. Bill Clinton took the state by pluralities in both 1992 and 1996; Dubya carried it relatively narrowly in both 2000 and 2004 (had either Gore or Kerry carried the state, they’d have won the White House). The Dems nearly swept all statewide elected offices in 2006, and it’s definitely winnable this year.
I like former Va. governor Mark Warner a lot, but I think he’d probably rather run for the Senate, which he’d be more certain of winning.
Sam Nunn makes Al Gore actually look exciting and dynamic, plus he’s been out of the public eye for a long time. Can’t see either Clinton or Obama picking him. If either goes for a Southerner - which I think would be wise - then Sen. Jim Webb of Virginia would be appealing, although he, too, is just in his first Senate term. (I agree with those who think that Macaca Man is toast on the GOP side).
I’ve always liked Dianne Feinstein, senator from California, but Cali is almost certainly in the bag for the Dem nominee, so she wouldn’t add much to the ticket. Hillary almost surely wouldn’t pick her anyway, as an all-female ticket would be waaaaaay too chancey.
Hillary might pick Tom Vilsack, former gov of Iowa, briefly a presidential candidate himself and a strong supporter of hers (and a graduate of my high school - woo hoo!). Barack might find either of two female governors good for the ticket - Kathy Sibelius of Kansas or Janet Napolitano of Arizona. Both have excellent reps, and are very popular in their states. Sibelius also has Ohio roots (her dad was governor for a term in the mid-'70s), and Napolitano just might bring Arizona into the Dem column (although probably not if McCain is the GOP nominee). Then again, Obama might decide that a black man at the top of the ticket requires a more boring white guy as Veep.
My two cents’ worth.