In Diablo 3 for the PC, PS3, and Xbox 360, it costs a bit of money to remove gems from socketed items. There is a way to get your gems back for free however if you don’t care about the item much.
If you take your socketed item to the blacksmith and salvage it, you’ll get the materials for salvaging, and you’ll also get your gem (or gems) back.
Obviously you don’t want to do this if you plan to sell your item, but if you’d rather have the materials from salvaging it anyway, then you may as well save a few bucks this way.