Willful is the American spelling of the adjective meaning (1) done on purpose, or (2) intent on having one’s own way. Wilful is the preferred spelling in all the main varieties of English from outside North America. Both spellings appear about equally often in Canadian publications.
Wilful is the original spelling. Though willful has been around for many centuries, it did not become common until the 19th century. And, as the ngram below suggests, it became the preferred spelling in American English around 1950. Willful, meanwhile, has slowly gained ground in British English, but wilful is still far more common.
This ngram graphs the use of willful and wilful in American books published from 1800 to 2000.