Ok, here is my guess 18 months out - the Democratic ticket will be Gore/Clinton. Here's why.
First off, Iraq is going to be an even bigger mess in '08 than it is now. Hard as this is to believe, I think this is the one prediction that is very likely to be true. Bush will keep trying to both prove he is right (more troops) and to leave the problem for whoever is next (no leaving).
Second, the Democratic congress will do an excellent job of both showing the country all of the mistakes, unethical behavior, etc of the Bush administration. And it will propose some good legislation to resolve many of the issues we face. But the legislation will get stopped between filibusters in the Senate and veto's from Bush. So all of this legislation will be bottled up.
What the people will demand is a candidate that they know can get the job done. This will not be like 2000 when many people figured it didn't matter who is president. This time it matters a lot. And as Kerry proved, it's not enough to be "not Bush" - you have to be a strong, compelling candidate.
Obama is out because he is an unknown. He represents promise and potential and youth. But he could also fall flat on his face as he has no experience and times like these are not when people are going to take a risk. (I also think he has peaked way too soon.) He could be the VP.
Edwards is out because he had a shot in '04 (as VP granted) and he didn't do anything. He wasn't a bad VP candidate but he didn't light up much besides the base and they will vote anyways. For this reason he doesn't even have a shot at VP.
Wes Clark seems like a natural for this. He does have the military experience. But he has not been able to gain traction as a candidate. In '04 he was run out and nothing... He is clearly running now and again no real buzz at all. I think he is there to be Hillary's VP to give her ticket more military and macho credentials.
And that brings us to Hillary (the rest are in the forget it category). The Iraq war will kill her chances. First off, she has no military experience. She's on armed services but she has never served in the military and has no real experience with the military. And she's a woman. That shouldn't matter but it will. In time of war the country is unlikely to look to a woman, and especially our first woman as president.
That leaves Gore. Military experience - check served in Vietnam. Executive experience - check was a very active Vice President for 8 years. Environment - he owns that issue. Boring, dependable, and capable is something the country will desperately embrace for '08.
As to the Vice President, I think we have reached the point where for a long time forward we will no longer see two white males on the ticket. Not with the talent available for Vice President. So the VP will be Obama or Hillary. (And either one would take it if offered - don't kid yourself.)
I think Hillary is the more likely one for two reasons. First she is a very well known quantity. Every piece of dirt that can be thrown at her has been. There are no secrets, no surprises. Obama has had an easy ride to date (remember his opponent Jack Ryan self destructing?).
Second, as VP all of Hillary's positives remain (fantastic fund-raiser, very popular with a large chunk of the electorate) while her negatives don't matter as much because she is the VP. People will vote for Hillary even as VP because in 8 years... But people tend not to vote against a VP.
Now if the Republicans put Condi Rice on as VP, then it will be Obama. But otherwise my guess is Gore/Clinton.