I'm surprised live bait would twist braid as Jeff stated or even a Mepps spinner.
Try it with a test. Borrow your wife's/GF's tape measure, trap an end between two fingers and wrap the rest around those same two fingers. At the end, pull the tape off like you were casting something. Result - twist.
When the line is wound back in, unless a spoon twists it back (forget swivels), the reel will wrap the line back onto the spool with the twists in it. Cast again, you've doubled the twists.
Why I say forget swivels, in general they don't work quite as well as you might imagine. They might stop a twisting spoon or deadbait from putting a lot of extra twists in the line, but they won't remove the line twists you've already put in. Been proven many times, honestly. A ball-bearing swivel works best, but they're usually quite large, more for sea fishing where I've used them band above all, expensive!
If I get line twist ( which rarely happens), I pull out a casting distance with the reel on the ground plus another 10' in the grass. While reeling it back in, with nothing at the end of the line, I hold the line between two finger near the reel. The rod guides and my fingers take any line twist out.
It's a good tip and it's the grass, not too short, nor too long, that removes a lot of the twist.
EDITED BIT: You know if you're using a spool of monofilament that has been used before, but maybe some time ago. You take a few coils of line off and then its starts to feel lumpy. That isn't deterioration of the line, but more likely where the twists having dried out for quite a while and have bedded into the line. If you use the line regularly, week after week, you probably will not notice it much.
EDIT II: Another misnomer I hear is 'wind-knots'. I do not believe in these. Using multiplier reels you never get them simply because you never get line twist because of casting like with an open faced spool. Line comes off as it goes on and v.v., it's always straight as it is with centrepins. I have tried testing this by blowing on my spools, shan't mention with which orifice, beforehand and it makes no difference. Do they mean 'wind' as in breeze, or 'wind' as in turning the reel? If the latter then YES!