Avenging Spirit

Avenging Spirit, known in Japan as Phantasm, 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. Players can possess one of four characters with unique abilities at the start of the game, but the library of enemies expands and changes with each level.

During a walk with his girlfriend, the player is ambushed by agents of a mysterious crime syndicate who take his girlfriend away and shoot him to death. Now, as a wandering spirit with the ability to possess most others, he is summoned by his girlfriend's father (who researches ghost energy) and is given a mission to save her from the mysterious crime syndicate that holds her hostage, enabling the player to rest in peace. (Wikipedia: The Free Encyclopedia, s.v. "Avenging Spirit")