I don't want my child to grow up thinking that every trip, whether it's WDW, the circus or the grocery store comes with a present. To me the vacation is the gift. I also don't enjoy shopping and don't want DS to think that shopping is an integral part of vacation. When we go to non-Disney places we might end up with a piece of clothing if it's something I know he'll wear on a regular basis, and we usually get a couple of post cards since I'm a terrible photographer, but that's it.
That said, for our trip I challenged DS who was 6 and had never successfully saved a dollar in his life to save as much as possible by telling him I'd double whatever he had at the end of his WDW trip. Well, he asked for money for his birthday, saved what the tooth fairy brought, asked me and my mother to pay him for extra chores and ended up with a little more than $100. I was amazed.
We left the money in the hotel room and made it through our first 6 days without him (or his godsister who was with us) asking for a single thing. It was so nice to be able to concentrate on shows and rides and not on shoping. On the night of day 7 we went to the big toy store in Downtown Disney. DS had about $220. He chose 1 $3 plastic pirate sword and announced that he was saving the rest. The sword broke that night so we went back the next day and returned it for a top ($4 I think). The next day in the park he bought an autograph book ($10 I think). He was determined not to break either $100 bill. His godsister (she had maybe $30 saved and I gave her $100 for her birthday since I didn't think it seemed fair for one child to be given $100 and not the other) did basically the same thing -- she picked out one very small item and saved the rest.
DS later spent his money on one of those cars that you sit in and drive, which came broken. He returned that and got a video camera which he loves and has gotten so much use out of.
I was really proud of both kids for choosing to save rather than spend and for not even asking for things at the park. DS's favorite souvenir is the
AAA luggage tag he got for "free" -- it's on his school backpack. That's plenty for him.
Because of that experience I don't think I'd ever buy my child Disney Dollars. The message that you have to "use up" the money in a certain place discourages saving IMHO.