I think Biden was the best possible veep choice given the field of likely candidates. The thing that bothers me most is his past (hopefully) and much-publicized predilection for plagiarism. If you've read about it (Slate has
two very good
summations), it's pretty discouraging. But that was 20 years ago, and many other aspects of his character outweigh those transgressions to me. David Brooks had a great op-ed in the NY Times this week highlighting why Biden is the man.
First and foremost, Biden has proven himself capable of intelligent and nuanced (if lengthy) discourse on all manner of issues. He's a sharp guy, even if he runs off at the mouth sometimes. One of Obama's greatest assets, on display in his books and his speeches, is his intelligent eloquence, and I think Biden will fit nicely with that, if anything strengthening it with a bit more pathos and outrage than Obama generally affords himself.
Biden also has something like the second or third lowest net worth in the Senate, estimated at $150k - $200k. In Washington terms (Hell, maybe even for CAGs), that's pocket change. He takes mass transit every day, and hasn't strayed far at all from the working-class roots from which he hails, despite several decades worth of opportunities to line his pockets. This puts him in prime position to highlight the hypocrisy of John "Ask my staff how many houses I own" McCain.
He also has an extremely compelling personal backstory, what with his wife and infant son dying in a car accident shortly after he was first elected to Congress at age 29. I think when you go through something like that, you can't help but be transformed by it, and you have a deeper understanding of what's important in life than someone who hasn't (although John Edwards didn't seem to learn much from losing a son and having a wife with terminal cancer). I'm not saying McCain, whoever he choses for VP, or Obama don't have that same wealth of personal experience to draw from, but if you ever hear Biden talk about that part of his life (and he only does so sparingly), you definitely get a feel for the emotional wisdom he gained from it.
On top of everything, he's got a ton of foreign policy bonafides, builds a bridge to the Catholics, and has been in Washington long enough to know where the bodies are buried. As long as he can keep his mouth in check, he's a great pick.