Gang Busters was a famous radio program that was first heard in 1936 and aired until 1957. The sound effects of police sirens, tommyguns, and screeching tires that opened the show were dramatic and exciting -- this inspired the expression 'coming on like gangbusters'.
Usage has opened up to describe things that are not just exciting, but successful, intense, and many other adjectives, and many drop the 'coming on like' prefix. I think we should be more careful about how we use it, and keep it true to its origin -- something that starts with much excitement and drama is 'coming on like gangbusters'.

Also used in conjunction with "like", to create "like gangbusters". This phrase can be used to describe something energetic or intense.

most commonly used in conjunction with "like" to describe something that is extremely effective

used to describe an action displaying a complete lack of subtlety

Used to describe the quality and size of surf.