When I recently wrote a post about mad and nutter I considered including one additional Britishism indicating insanity. I ultimately decided not to because the chance of any American using seemed closer to slim than none.
I did not count on the New Yorker. Reading the August 1 issue of that publication this morning, I came upon this sentence from Sasha Frere-Jones: “My Morning Jacket, on the recently released album ‘Circuital,’ its sixth, makes it clear that the real hippie is neither biddable nor daft.”
That’s right, daft. Wikipedia informs me that Frere-Jones is an American, Manhattan-born, though it also notes “he is a grandson of Alexander Stuart Frere, the former chairman of the board of William Heinemann Ltd, the British publishing house, and a great-grandson of the novelist Edgar Wallace, who wrote many popular pulp novels, though he is best known for writing the story for the film King Kong.”
Turning to the New Yorker’s merciless online database, I find that Frere-Jones has used daft eleven times since 2005. This gives him a narrow lead over the magazine’s (American) film critic David Denby, with eight.
notoneoffbritishisms.com 
I would be daft to think that most americans use “daft.” More than likely: “nuts,” “crazy,” “cuckoo,” or a longer locution such as, “Are you out of your mind?” That said, I like daft, and would vote for its inclusion ih the American canon. One caveat: The New Yorker may be unique. I often come across British words and phrases that I tend to never see in other publications.
“Daft” implies a kind happy-go-lucky idiocy, rather than mental instability. “Acting daft” is certainly behaviour that departs from the straight-faced norm, but arising from a lack of self-awareness rather than insanity. cf “daft as a brush”, “you big, daft ha’porth”.
“Mad” = insane. But it can be used as a compliment for someone who displays an admirable devil-may-care attitude.
A “nutter” is potentially criminally insane and should be avoided. Not at all the same thing.
“daft” is similar but not the same as “crazy” or “insane”. It’s usage is much softer, closer to “silly”. It’s often used as a term of endearment. Seems to derive from northern english/scottish dialectal use.
“‘that lad, ‘e’s daft, ‘e is!” i.e. he’s silly, or not quite right in the head. But not necessarily insane. “Insane” and “crazy” are pejorative, “daft” is not.