16 days for us. We did that many days in summer 2014 with 3 kids (D13, S11, S08). We did multiple split stays at 6 different deluxe or dvc resorts. It was incredible and never got boring. Spreading it out like that allowed us to not have to rush around (one of the bonuses now with having FP+). We could enjoy each day, as well as spend enough time experiencing the amenities at each of the resorts, and work in several days at the water parks. It was perfect.
This summer, we will be doing 15 days, although the first 4 will be at the Hilton Head Island DVC. Afterwards we will trek down to WDW for the remaining 11. We can't wait.