When we went in 2008, my DS was 7 and DD 5. We rented a double stroller just for EPCOT one day because it can be exhausting to walk around World Showcase, expecially on a hot day. I think it was the third day of our trip.
And then in 2010, my DD was 7 and had the stomach bug on the third day of our trip. By the fourth day she was feeling better but we rented a stroller at AK for her and pushed her around in it. If people gave me weird looks, I really didn't notice, nor would I have cared.
On a normal day, MK and DHS are fairly easy to get around in, plus you stop and wait a lot so I don't think you'll need a stroller for these two parks. As for the other ones, play it by ear and see how your kids feel. If they seem to be whiny and losing steam, you can always rent one. And trust me, nobody will be pointing and laughing at you at the park for doing so, as some on here seem to want to make you think.
Have fun!