This is one of the most unique tools for removing a cork.
The "Ah-so" cork puller was once the rage in California.
The device has two prongs that are wiggled between the cork and the bottle neck, and with a quick twisting motion, easily yanks the cork out of the bottle without puncturing the cork. Most of the time.
They work best on new American corks which have been lightly lubricated before insertion. On older, saturated European corks, they can punch the cork into the bottle if you're not careful. The "Ah-so" works fine, but requires skill and practice. There are several brands ranging from $4 to $7. I don't recommend them for beginners. You can find one here.