Amok is the dictionary-approved spelling of the word meaning (1) in a frenzy to do violence, or (2) in an uncontrolled state. Amuck is the original English spelling of the Malaysian loanword, which has been in English for several centuries, but it fell out of favor by the middle 20th century.
Examples
A few usage authorities still recommend amuck, but amok is now far more common and is preferred by most major publications—for example:
I also love running amok at De Kaaskamer, the ideal spot for a tour of Dutch cheeses. [NY Times]
Images of drunken language students running amok on Malta’s streets and having sex on the beach made headlines last summer [Guardian]
Most of the commentary has been to the effect that this is an example of the nanny state run amok. [Wall Street Journal]
As a teenager, he endured his fair share as he ran amok with his mates. [The Australian]
Ngram
This Ngram shows that amok became the standard spelling around 1950 and now prevails by a large margin:
