I think that it really depends on the child. Every one is different.
My oldest went for her first time at the age of 5. She did not use a stroller and did just fine in the parks all day long.
However, we took strollers for our youngest three children. In December 2007, we took 3 strollers for our kids aged 7, 5, and 3. Our 7 year old is a tiny thing, we are always trying to get weight on her and we really didn't think she could handle walking around that much. She did walk partly, and rode when tired.
On our last trip in October 2008, we only took two strollers, but really used one for our youngest. She would walk sometimes and if the others were tired they would ride for a bit.
On our next trip, we are finally not taking any strollers. Yay! It will be so easy not to have to worry about parking and carrying them. But it will be a pain to not have anywhere to store a drink or a sweatshirt.
Bottom line, you know your child, no one else does. Don't let someone judge you when they don't know your unique situation. If you think your child would benefit from a stoller, bring one.