I don't know the ages of your kids, but it saves you a ton of money, if they understand that the money they bring - say $120 or whatever amount of Disney$ they have - is their total allotment for the trip. When the money goes, that's it! They actually give a lot more thought to what they want to get. Also, instead of 10 little souvenirs, they may opt for one or two big ones. So much of the stuff is very expensive, even the little light-up toys etc. are in the $15-$20 price range. The hardest part is letting them buy whatever THEY choose.
When my nephew was 12, he wanted to spend $95 on a watch. He was horrible on watches at the time, always breaking them. We pointed out that we didn't think it was a wise choice, but it was "his" money so we let him spend it as he desired. Well, he bought the watch, but before we left, he gave it serious consideration and returned it.
What I really like about this scenario is that they know up front how much they can spend and they really are much more discerning than if I'm buying them something at every souvenir stand. And when you ask them, "Do you really want to spend YOUR money on this?", they actually give the purchase some thought.