The last I went, any games in which you won tickets that you could exchange for prizes were an extra charge (kind of like Dave & Busters/Gameworks, etc.). I believe your ticket came charged with something like 40 credits (games are between 1 and 4 credits usually), but I could be off on this. Any more and you have to add money to "recharge" your card. However, there are a lot of games that are free as well.
Additionally, anything you purchase from the create zone will cost money. You don't have to pay to create, but do if you want to take it home. Some include making your own CD, cartooning, Sid's Create-a-toy, the one where you warp your face, etc. All these you can play with and see your finished product (or hear it!) on the computer before you decide to buy. Most were about $10 as I recall. You can also purchase your video of your ride on Cyberspace Mountain and there are places to put your face on (Disney) stickers and things like that.
And of course the gift shop and places to eat - Cheesecake Factory (I think is the name) has awesome desserts that you won't be able to pass up.
If you have young kids, there's more than enough to do without spending any extra money if they don't realize they can buy the things to take home and just do the "rides" and create and play the free games. Adults can set a budget. Probably hardest with the 'tween market who of course want to do anything and everything that costs extra! Maybe have them bring their own money!
Side note - when DQ first opened in Chicago, nearly everything was included free! All the games were free, stickers, etc. We went one day and got over 8000 tickets in the arcade and came home with tons of prizes (basketballs, mini air hockey, and tons of DQ logo'd stuff). Also made sheets and sheets of the stickers in all the various pattern's, etc. Guess it was because of people like us that they went to pay-to-play!
