The serpentine belt on my 2001 sport with AC slipped yesterday and came off the pulleys. It looks like it's still in perfectly good shape, no frays or tears or cracks. Can I just put it back on and fix the tension or do I need to replace it once it's slipped off? Thanks!

 

Harmonic balancer or seized pulley, belts don't just fall off.

 

Yeah, I need to check all the pulleys tomorrow to make sure that nothing is seized up (or figure out what is), but pending fixing whatever it was the caused a perfectly good belt to slip, can I reuse it?

 

Depends on its age and condition. Inspect for cracking, fraying and exposed nylon threads. Also for glazing. If you replace it I suggest a Gatorback belt, $30.
But I am curious as to the how and why. Something is wrong for it to come off.

 

If it's not cracked & weathered sure you can re use the belt. But a new belt is like $25 so it's cheap enough to just replace it, and keep your old one for an emergency spare.