If you need to mince garlic, smash it - don't peel it. Unless you need the garlic clove whole, just smash it with the flat side of your knife. The peel breaks apart so it's easy to remove. Mince away!
If you do need whole peeled cloves, try this: Drop whole cloves into a lidded bowl, cover, and shake vigorously. The peels often fall right off. (This only works about half of the time, but it's so cool when it does that we had to pass it on.)