Let’s Play Star Trek: 25th Anniversary! 
Admittedly kind of a random title for an NES/Star Trek/any game, but this is actually a pretty awesome game. Sort of maybe following the plot of the whale Star Trek movie (4 maybe?… I’m no trekkie), the idea is that Kirk and the crew have to go back in time to right specific mistakes of the past.
Let’s Play Star Trek: 25th Anniversary:
I remember trying to play this with two different Mikes who were my best friends over various points in my life, though ultimately neither was especially interested in the game.
That leads me to believe that I may well be in the minority in digging this game. My brother and I got this game late for the NES, so we didn’t grow up with it and have that bond over it, but we definitely appreciated the scope that this game seems to pull off. We must have gotten it in the age of the internet, because I’m not sure how we would have figured out the majority of it without it. I just make it a point to ask him what he remembers about this game.
Anyway, this game is very story and puzzle based and less action centric. You have to solve a number of puzzles with various members of your crew to advance the plot and a lot of it isn’t especially obvious. As you can tell from the let’s play Star Trek video I did, most of it isn’t obvious even with the aid of the internet and memory. Damn memory.
Good game though, and although my various best friends over the years didn’t get the charm of this game, I still have strong fond memories of it.