Yep, white vinegar is GREAT for getting the musty smell out of towels and stuff. It's also good for greasy counters and stove tops. The smell goes away pretty quickly taking other smells along with it.

I've had great luck using it when I've done dumb shit like going on vacation with something stinky in the fridge. Pull everything out, toss what's bad, spray the shelves with a 50/50 vinegar and warm water solution, let it sit a minute, and wipe it up. Then pop everything back in. It just kills the smells.