We got a double stroller for big parks (Epcot and MK). We also used one the night of MVMCP. Our girls were 8 and 4. There was no need for one at Downtown Disnery or at POR (where we stayed). You can rent stroller for the week and get a discount. If you park hop, you turn in stroller as you leave one park and simply get one when you arrive at next park. The stroller stations are conveniently located near the front gate of each park.
my parents renting strollers when we went to WDW up until I was about 9 yrs. old. I even have a few old photos of my mom using the stroller as previously mentioned with me sitting on her lap!
Strollers for kids up to age 8 or 9 are really nice!