All the time. And for perspective, my DD was a kid who NEVER got in her stroller after she took her first steps at 12 months old- not at the zoo, not at the mall, not anywhere else that involved a lot of walking. The only place she ever rode in a stroller after taking her first steps was at Disney.
On her first trip when she was 2, she pretty much took one look at how big the place was and jumped in her stroller and let us push her around which was unheard of for her. I can't even imagine trying to negotiate WDW with a 2 year old without a stroller. We were able to stay in the parks from open to close and she took stroller naps (we tried to take a resort break the first day and quickly discovered that did not work for her- she was mad that we left the park and refused to sleep for about 3 hours until we went back to the park and then she got in her stroller and went to sleep). The stroller is particularly helpful if you are trying to move quickly to get to an ADR, FP, or show. 2 year olds do not move quickly. I think you will use it way more than you think you will.
One other note- do you have connections flying? You might want to consider taking a small stroller with you instead of renting at WDW. We found the stroller useful in the airport- particularly when we had short connection times (either by flight booking, or more often by the first leg of our flight being late). Also, where are you staying and how are you traveling around WDW? If you have to turn the rented stroller in when you leave the park, you might find yourself having to carry a sleeping or sleepy tired child from the turn in point to the bus stop/boat stop/ monorail/ walking to the resort/ as well as once you get to the resort through the resort and all the way up to the room. You do have to fold the stroller for the bus, and for some (but not all) the boats, but it also can come in handy outside of the parks.
I think our first trip without the stroller was when DD was 6 (she just turned 13), and I would say that was our worst Disney trip in all the years we have gone (and we went when the parks were closed and we got stuck in resort for a hurricane). She is high energy, but did not yet quite have the stamina for all the walking involved and was whiny and complained her feet and/or legs were tired a lot. By the time she was 8, she could go open to close on her feet like a pro!