One of my favorite games for the NES is one I never actually owned. I mostly played Bugs Bunny's Crazy Castle at my cousin's house at Christmas, but I still liked it a lot more than most of the games I wound up eagerly buying. I never had a chance to read a player's manual, but the gist seemed to be Bugs is caught in a castle with many enemies who want him dead, and must make his way to the top, where he presumably escapes somehow. On each floor he has to grab all the carrots without getting touched once.
The player can opt to try and elude the enemies (including Daffy and Yosemite Sam, among others), or take advantage of weapons that may be scattered about. There were boxing gloves to fire at enemies, and various heavy objects which could be pushed over ledges to K.O. unsuspecting types below. So there was a certain amount of strategy, because you needed to figure out how to get to the carrots without getting trapped, which could take the form of maneuvering enemies to where you could dispatch them, or simply get them out of position. It's not a complicated game, but there were different ways to approach things, which meant I could change my style to suit my mood*.
I have a soft spot for the music too. It's not anything deep, but it works well, in part because I think the music's beats are matched to Bugs' stride. The music sort of works with him.
* I do the same thing with Thief: Deadly Shadows, opting to make it through with as little violence as possible sometimes, but other time deciding to give every person I see a blackjack to the head. Either way gets the job done, so it's all about which is more fun at the moment.