I'm pretty sure this has been asked in the past (perhaps by me) but it's been a LONG time and it's the kind of question where the answer could change based on the day/week it's asked.
Here is mine:
Drums: Glenn Kotche -Amazing musician, great drummer and percussionist. He seems to be always searching for new ways to make percussive sounds in studio. Plus the guy is amazing live. I chose him in spite of the fact that when I recently left my wife (last minute) to drive to NY and see them play, he signed a poster to her saying, "he wished she were there." -He knew he was getting me in more trouble.
Guitar: Since I can't very well reconstruct Wilco (I would say Nels), I'll go with Richard Thompson because the guys a bad-ass and I think he'd be a good fit with the rest of my picks.
Bass: Without a doubt Paul McCartney. -what a bulldog! Most people don't realize how hard the guy works to get a baseline perfect. Even if you're not a McCartney fan, you can't read Here There and Everywhere by Geoff Emerick and not be impressed by his work ethic. But to me, his bass lines are so melodic, in the pocket and... well, McCartney-esque. -He is his own style.
Vocals: EDIT: I'm no longer going with Stuart Murdoch of Belle & Sebastian- he's great and all but this band needs more soul and showmanship. I'm going with Mick Jagger -Doesn't get any better really.
I'd love to hear that band. What's yours?