The moderate resorts have a separate category for king bed rooms, the others it is only a request. As twodogs said, DVC 1 bedrooms and larger have king beds in the master except Tree House Villas.
At the values, the king bed rooms are the same price as the other rooms (within the same category, i.e., a "non-preferred" room w/king bed is the same price as a "non-preferred" room w/o king bed). It's only a request though and not a guarantee.
Unless you specifically book it, it's just a request if you ask for one. We requested a King bed and did not get one staying at a value. We ended up sleeping in separate beds for the most of the trip because the beds were so small. Just be prepared!
I said (MOST) Most of the king bed rooms are set up for Hand-di-cap wheel chairs. Large slide doors for wheel chairs in bath rooms, and extra large room doors.