Strollers
Disney rents strollers at $8 per day for a single, $15 per day for a double. If you return the stroller at the end of the day, they will rebate $1.
Disney offers a discount of 10% (or more) for multi-day
stroller rentals. A multi-day rental will also save you time, because you'll be given a receipt that allows you to go up to the cast member dispensing the strollers, have them stamp your receipt, get your stroller and youre off! No more waiting in the long cashier line to pay for a daily rental. In addition, they will refund any unused days. Thanks to Julie S and Lisa C for additional info.
Hold on to your receipt! If you misplace your stroller, present the receipt and they'll replace it without charge. Also, the fee covers rental for the whole day, even if you "hop" between parks on the same day. So if you start the day at one park and then move on to another park later, keep your receipt from the first park and present it at the stroller rental. They'll issue you a stroller at the second park without additional charge.
Bringing your own stroller will, of course, save you quite a bit of money. However, this may be counterbalanced by the hassles of getting it to Walt Disney World and then loading it on and off buses, monorails and boats (if you use Disney transportation) or in and out of a car trunk (if you'll have a car at Disney).
If you want to avoid the hassle of transporting a stroller on a plane, you might consider buying a cheap one upon arrival and giving it to another lucky family when you leave.