I hang onto them...save them for the next trip or use them at the store when I don't have any cash on hand. They spend just like cash, but are safer...When I was married to the ex, I used them as a way to save money without his knowledge...he was a super tightwad...that way if he found them and took them I could report the theft and get my money back.
Here's a hint for kids...we've been using the 2 signature traveler's checks with DS since he was old enough to sign his name. This way he knows exactly how much money he has to spend and becomes responsible for it...when it's gone it is gone. Also, we feel better about him carrying them than cash. Plus, he thinks he's a big shot using traveler's checks.