When you think of identity theft, you probably think of people using credit cards that are in someone else's name. Though this does happen often, it really is just caused by cashiers who are too lazy to check the back of the card, demand identification, or check that signatures match exactly.
Sometimes, the cashier themselves may write down or memorize your credit card number for use at a later time. Though this is now considered one type of identity theft, there are a few more that have a more dramatic impact.
Drivers licenses are a very common way you can have your identity stolen. This doesn't cause that much damage and is very easy to fix. The most common thing someone will do with your drivers license is alter the photograph so it looks like them.
This is very difficult so if someone goes through all that trouble, odds are they have a warrant they want to avoid. The problems arise when they get a speeding ticket or any ticket that doesn't send them to jail. They will disappear and you will find yourself having a warrant from somewhere you may have never been.
The last thing you want to happen is to be on your way somewhere with friends and family and find yourself in jail for a crime you didn't commit and have no knowledge of.
It can be very difficult to prove that this person wasn't even you and you might have to find the officer that issued the ticket. That could take a while and you might spend days in jail until you can be bailed out or the issue is resolved.