The Movie Monster Game is a 1986 computer game by Epyx. It was released for the Apple II and Commodore 64.
The game offers a variety of scenarios, playable monsters, and cities to demolish (complete with famous landmarks, such as Tokyo Tower). The monsters are based on popular movie monsters such as The Blob, Mothra, and the Stay-Puft Marshmallow Man, and Epyx was able to secure licensing for Godzilla.
The monsters in this game include:
Spectra ( a giant wasp)
The Glog (a huge green blob with red eyes)
Tarantus (a giant Tarantula)
Mr. Meringue (a knock-off of the Stay Puft Marshmallow Man)
Mechatron (a giant robot)
Source: Wikipedia, "The Movie Monster Game", available under the CC-BY-SA License.