I'm assuming the problem is with spinning gear?
If so there are a couple things you can do to get rid of it.

Normally when I spool a spinning reel, First I make sure the line is coming off the filler spool counter clockwise, once I fill my reel, I go out to the yard where I have a barrel swivel tied on one end to a piece of fishing string which is tied to the fence, I just leave it there.

 Then I take my new line on the rod and tie it to the opposite end of the swivel.
Open the bail and walk off a lot of line about 2 or 3 cast worth in distance. Then I close the bail and reel up the slack and slowly walk back to the swivel while continuing to reel keeping the line tight, while your doing this the barrel swivel will spin getting rid of any twisted line that was out in those 3 cast worth.

 Another thing which is important is to never turn your reel handle while drag is being pulled from your reel, wether it's a fish or a snag, if you have a 5.31 reel ratio everytime you turn the handle while the drag is being pulled out will put 5 twist in your line.

One last note which I just put to use last week and it worked. when you go to make a cast and it doesn't go anywhere and you look at your reel and you have that ugly loop, and you know if you open the bail and pull it your going to end up with three different lines coming off and a big mess.
Well don't even flip the bail when you see that loop, loosen up your drag some and just start pulling the line off. when you get to the spot it will just come out. I don't know the science to it but it worked.

Hope those tips help with some of your problems

There's a difference between spool memory and line twist.  If you have twisted line,..you just have to unspool it and get rid of the twist that's there.  Use Joe's method (but make sure it's a quality swivel,.. the cheap ones have too much friction and don't work too well..) or if you're on the water,..just let the line out without a bait behind a moving boat.  It will untwist itself as it drags through the water....then simply reel it back up and you'll be good to go!

For eliminating/minimizing the spool memory,....first use a good limp line like Pline cxx or fluoroclear.  Then give it a sray periodically with Reel Magic.

If you're using spinning gear,..always close the bail with your hand and NOT BY CRANKING!!!  Every time you crank to close the bail, you put 1/2 of a twist into the line.....(so after 20 casts,..you would have 10 twists in the line.)

If you still have headaches after all this,..you may want to try using some 20# Powerpro braid on that spinning reel.  It is very soft and has absolutely no spool memory.