If your finger is so swollen that you can't get your wedding band off, this hospital trick might be just the ticket. All you need is an elastic band.
The first step is usually to try a lubricant such as Windex, but this method -- while a bit complicated -- should work too. Essentially, you wrap the elastic band tightly around the finger and move it towards the ring. Once you get to the ring, try to feed the band through the ring. Once you do, you should be able to start unwrapping the elastic, and it will bring the ring with it. Check out the video to see it in action (skip to about 1:35 to get to the demonstration).