Don't rush to cut the ring off. There are many things you can try first. Here are a few that we've has great success with.

These ideas work best when you keep your finger as straight as possible. Sometimes holding your hand above your head for a minute or two will increase your success. Also, soaking your hand in ice water can help in reducing any swelling.

Lubricating

1. Spray the ring and finger with window cleaner.
2. Turn the ring around a little and spray it again.
3. Gently pull the ring off the finger.

Instead of window cleaner you can use butter or other cooking oils. Be sure to wash your hands afterwards.
Having help from someone else makes it easier too. The other person can slowly twist the ring while you continually spray the ring. If the swelling is severe you can apply Preparation H or similar products to the finger while keeping the arm higher than your shoulder.

Dental Floss

1. First you need to get the floss under the ring. A piece of negative film works good.
2. From the ring to the finger nail, wrap the floss firmly but not tight around the finger.
3. Next, grab the string (closest to the knuckles) firmly so the string is taunt.
4. Begin to unwrap the string. The ring slowly inches it’s way off.

Plastic Wrap

This idea was found on the internet. Primetime Gold Jewelry hasn't tried it but it sounded like a great idea. If none of the tips here worked for you, searching the internet may uncover a method that will.

1. Wrap the finger from the ring to the fingernail with plastic wrap as tight as you can.
2. Apply lots of any type of lubricant you have to the ring and finger.
3. Grab the plastic wrap and ring very firmly and pull the ring off.