We just got back from wdw and I am so glad I brought my double stroller for my 3 and 5 yr olds, because:
(1) you a have stroller at the airport which allows you to move ahead in most security lines,
(2) didn't have to wait in line to
rent a stroller,
(3) we stayed at the poly so we just wheeled them onto the monorail and back to hotel when they fell asleep,
(4) your own stroller is waaaaay more comfy and cleaner than the rentals -- they are made of hard plastic -- and not that I am a germaphobe, but yuk -- public strollers...imagine all the ice cream and other stuff that's stuck on them, and
(5) Disney is obscenely expensive, why not save $18 bucks a day.
IMHO, I just liked having my own stroller...Although, if I didn't have a double and was only going for 1 or 2 days, I would rent. Hope this helps.