Avenging Spirit
Avenging Spirit, known as Phantasm in Japan, is a 1991 2-player platform arcade game developed by C.P. Brain and published by Jaleco. Players attack (or possess) enemies, collect power-ups, and defeat bosses to advance. At the beginning of the game, players can own one of four characters with unique abilities, but the library of enemies expands and changes with each level.
Story
During a walk with his girlfriend, the player is ambushed by agents of a mysterious crime syndicate who kidnap his girlfriend and shoot him. As a wandering spirit with the ability to possess most other people, he is summoned by his girlfriend's father (who researches spirit energy) and is tasked with rescuing her from the mysterious crime syndicate that is holding her hostage so that the player can rest in peace. (Wikipedia: The Free Encyclopedia, s.v. "vengeful spirit")