Disney Dollars, and the new Disney Gift Card (which came out in early 2006) can be used at any Disney-owned venue in the WDW and
Disneyland parks and resorts, including shops, stalls, carts, restaurants, eateries, Pleasure Island clubs, bars and lounges at the reosrts, and at resort front desks for paying off your balance.
The gift cards, of course, have one small limit - they can only be used at venues that have electronic card readers, which lets out a few of the smaller drink and snack vendors.
Shops in the Swan and Dolphin and the various Downtown Disney area hotels cannot accept either DD$ or the gift card, since they are not Disney owned.
At least some of the Downtown Disney West Side shops cannot accept them, either, including the Cirque de Soliel and the AMC PI 24 Theater.
I have been using DD$ at WDW for years; in fact, for my last 4 trips I have used them as a method of saving - I pick up $20 in DD$ per payday and sock it away. I love DD$ and I love making the bi-weekly pilgrimage to my local
Disney Store as part of my year-long trip preparation.
However, DD$ have one Achiles heel - if you lose them, they're gone forever. The new Disney Gift Card does not have this Achiles heel, because it can be replaced as long as you have the original purchase reciept, just like a lost park hopper or lost KTTW card. Because of this, my next year's trip savings will be entirely on the gift card instead of DD$. I will also feel more secure carrying that card with me through the airports than I do carrying hundreds of dollars in DD$, since DD$ are only available in denominations of $1, $5, and $10 at my local Disney Store (there was a $50 note issued during the Happiest Celebration on Earth but my Disney Store never got any).
Also keep in mind that whether you save up via the gift card or DD$ that you can put them down instead of a credit card to enable room charging priviledges when you stay at a WDW resort. This allows you to charge things to your room instead of carrying your DD$ or gift card around with you.