We have not been brave enough yet to take DD's power wheelchair to WDW.
There are some rides where are wheelchair users need to transfer (and, of course, she would need to transfer for those).
Here's a
link to a page from the official Disney website that lists the rides where wheelchair can be used on the attraction. You'll find a link at the top of that page to the Guidebook for Guests with Disabilities. There is one for each park and they give some (basic, not very complete) information. You can pick up a printed copy at Guest Services in any of the parks. For the rides where a manual wheelchair can go on, you should be able to get a power wheelchair on, as long as it is no bigger than a manula wheelchair.
There were a few rides where we had problems getting DD's manual wheelchair onto the wheelchair car. Or specifically, we had problems getting DD's manual wheelchair with her overstuffed backpack hanging on back of it on the wheelchair car.
Here are the approximate dimensions of her wheelchair:
width 25 inches
length with bag 50 inches
length without bag 43.5 inches
The length measurements are from the very back sticking out part to the end of her shoes sticking out over her foot plates.
There was extra room in the width, but not much in the length.
(Her bag was not so big as it sounds, but her new manual chair has a bar along the back that keeps the bag from fitting snugly against the back of the chair).
With the backpack on, the car door (behind the wheelchair) would not close; once, we took that backpack off, the wheelchair fit. Specific cars I can think of that we had problems with were:
Imagination
Buzz Lightyear
Aladdin
Triceraptop Spin
Great Movie Ride
We never got on Pooh this trip, but I know the car is about the same size as Buzz.
On all those rides, a part of the car folds down to make a small ramp, you drive up the ramp and into a wheelchair parking spot. Then the ramp (or another part) closes behind the chair to make a door that keeps the chair secure.
We also rode on the wheelchair car on:
Great Movie Ride (a tight turn, but did fit)
Living With the Land
the ride in Mexico
Small World (pretty much same boat as Mexico)
WDW Railroad in MK
Kilimanjari Safari
We didn't go on the Jungle Cruise (so we haven't tried out the wheelchair car there). We also didn't go on Ellen's Energy Adventure this trip, but we have on past trips without a problem.
One queue that might be difficult with a power wheelchair is Living Seas; it's wind-y with a lot of curves.
For the Pirates, you need to transfer to a manual wheelchair (they have one at the entrance) for the line and then transfer to the boat. Peter Pan is a ride where you need to transfer, but the moving walkway can't be stopped at all.
