The Allagash is an iconic wilderness canoe trip. During the summer the river is downright packed with guided trips, private trips, and groups from summer camps.
The primary whitewater on the Allagash is Chase Stream Rapids (Class II). Chase Stream comes immediately below the dam at the outflow of Churchill Lake. These moderate rapids run for about two miles before flattening out. Many canoe trips elect to have the rangers at Churchill Dam portage their food and equipment around in a truck before running it with empty boats.
The other prominent drop is Allagash Falls, a large Class V that is portaged by all the canoe trips. Allagash Falls is likely runnable, though you'd have to be very enthusiastic about the logistics of getting a creek boat deep into the woods for a relatively short bit of paddling. It has
been swum accidentally, and knowing New England kayaking history someone may have run it many years ago.