I'm sort of the opposite of most people... We brought a stroller on our trip in December and I honestly found it to be a huge pain!!! The only time it was really super useful was naptime... DS(2) napped in it every day...sooooo, we had to have it for that. Otherwise, you have to park it in "stroller parking" every time you ride anything so mostly it was only used in traveling from land to land... Then we would park it and DS would walk around with us to different attractions.
That said, there are certainly times when we NEEDED it - like nap time. Sooo... for our trip in the fall, we are considering renting a Disney one so that we don't have to deal with it on buses, throughout the parks, etc. until we really need it...
I certainly wouldn't bring/buy or rent anything larger than a basic umbrella stroller. Getting them on and off the buses and even finding parking at times is a pain, so I was super glad to have a little bitty, easy to fold umbrella wal-mart cheapie. If we don't rent this fall, I will bring it again. I also liked that I was not worried about the possibility of it being lost or damaged so I didn't hesistate to "park" it whenever we needed to.
Ultimately, I think the stroller issue is really a personality thing... what are you comfortable with? What is your touring style, etc.? (We were pretty gung-ho and were in the parks at least 10 hours a day darting from attraction to attraction most of the time... the fact that parking the stroller slowed us down was frustrating to me! If we were going at a slower pace I might not have minded a bit!)
Hope some of that at least helps!