In The Real Ghostbusters episode "Station Identification" there was a Star Trek spoof done. Well as you can see below the ship is not the Enterprise or atleast they didn't base it on it...
Otherwise, Paramount Pictures studio would issued a C&D order to prevent it from being aired if an unauthorized likeness of the USS Enterprise was used in the RGB episode (unless they got proper permission/clearance with PP studio for a Star Trek parody beforehand -- looks like it was cleared considering that it has a vague likenesses of Spock, Bones, and of course, Jim). The ending credits would have stated PP studio for proper credits.
I don't recall seeing/playing any arcade or console based shmups with that particular generic spacecraft design though. Yes, I do see some of the similarities of that generic design compared to the Star Trek one.
Ever notice how in the Transformers cartoon, with the introduction of the new Autobot character Skyfire, his likeness isn't the same as that of the original Jetfire toy that Hasbro released? That's because Hasbro entered an agreement with Bandai not to have the famous Macross Valkyrie Fighter mecha shown on that particular series as it would be a breach of copyright infringement. So thus the name change to Skyfire from Jetfire and an all new jet design + robot design indeed. Of course, in the original Transformers Jetfire toy commercial, there is an animated Macross VF version of Jetfire battling it out with some Decepticons.
PC Engine Fan X! ^_~
Last edited by PC Engine Fan X! on Sat Nov 05, 2011 6:20 pm, edited 1 time in total.
There was an old shooter called Megamania whose player ship was obviously modeled after the Enterprise, but that's about as close as my knowledge comes to what you're talking about.