The parks at WDW have nice strollers to rent these days, singles & doubles. We always took an umbrella stroller to DTD if we needed it, but renting them in the parks sure does save on a lot of hassle. No dragging them on the buses, and no hassle when you are going through the turn styles at the parks.
On that note, if you do rent strollers at the parks, take some sort of sash or ribbon to tie onto the handles. There are so many strollers rented there that when you park them for rides and such, it makes it a lot quicker and easier to identify which one is yours when your ready to take off again.