Based on the evidence of the past weekend. people keep their kids in strollers up until age, I dunno, 9! We were there with a 5 & 7 year old and had never considered having a stroller as we don't own one anymore, and thought it would be a pain to drag around. Having seen many people struggling with strollers on transportation and in the parks, I definitely would never recommend one for a kid over age 4 unless they aren't used to walking at all.
We had to put the 5 year old on our shoulders a couple of times, and on our "late" (9pm) day I took her back to the hotel for some downtime in the afternoon. Other than that it wasn't a problem for them to keep up on our pretty vigorous schedule. The 5 year old complained a few times, so we found ways for her to get little breaks while in lines, gave a few shoulder rides (as mentioned) and took her to shows when her brother was running all over doing Sorcerers of the Magic Kingdom. We also did
Disneyland without a stroller when they were 3 & 5, but obviously that's easier (and she got a lot of shoulder rides then).