Mr. Gimmick

Developed by Authentic Entertainment and published by Sunsoft, this game only saw a Japanese and Scandanavian release.
It is said to be one of the best games never released in the USA. The cartridge contains a special chip that allows it to have more music channels, giving a better experience overall with a high class music track that is competitive with that of Blaster Master.
In order to get the best ending(which I did), you have to find each secret item hidden on the levels and also beat the game without having to continue. If you do not achieve this, the game ends with a sad ending after the Ghostfather boss is beaten.
The controls do take getting used to as a somewhat physics engine is in play since the star will actually bounce at different velocities and heights depending on where you are shooting from.