Apparently vodka takes away the pain in more ways than one. Cocktail expert Miss Charming lists several uses for vodka (besides drinking it), including this gem:
To remove a bandage painlessly, saturate the bandage with vodka. The solvent dissolves the adhesive.
Haven't tried this technique myself, but next time I've got a Band-Aid on, instead of the fast rip-off approach I might reach into the bar first. Check out Miss Charming's vodka page for more ways to use vodka around the house to clean and more.