What can I use to take off a ring on my middle finger without cutting my finger off, or damaging a precious ring my dad gave me?

Here's a video of the dental floss trick:

http://www.dailymail.co.uk/video/virals/video-1100...

If the excellent suggestions by oikoσ and MsBittner fail then most jewellers have a special ring cutter tool. It uses a nearly razor-thin cutting disc to safely cut a very fine and thin cut in the ring causing minimal damage which is not only easy to repair but can be the first stage in getting additional metal soldered into the ring to enlarge it. Done properly, the repair and any extra added metal are completely invisible afterwards.

Get cold all over, which will reduce any summer-related swelling of your fingers. (My fingers are much bigger in warm weather.) Still keeping chilled, elevate your hand for five minutes. Use a liquid soap to lather it up and see if the ring will slip off.

There's also a method involving wrapping it with strong thread (search online), but I've never tried it.

Get some strong, thin string (fishing line is good) and start winding it a round the base of your finger. When you get to the ring, thread the string through the eye of a needle and pass it under the ring. Continue winding. The ring should slip off. It might also help to lubricate your finger, including the part under the ring or to dip your finger (but NOT the ring) in ice-water.

If pulling it off with your fingers doesn't work, the ring is ALREADY damaged.