Way too many, and it's less to do with the quality of the games, and more to do with my shite memory. There's easily a couple dozen from the nes that I've forgotten I've even played, let alone beat. Hell, I had to go through a boxart list to even remember half of the ones I have listed here.
Nes:
Bayou Billy: You are a guy with a knife, and there's some crocodiles.
Disney's kingdom. I only vaguely remember 2 levels; A spooky 2d platforming area, and an outerspace ride, where you had to memorize when to choose the left or right path.
MC Kids: You could high-five the character at the menu to change characters. That's it.
Ninja Gaiden: You could wall-cling, and there was a train section. If that was the original, or one of the sequels, I couldn't even tell you that.
Roger Rabbit: I remember often falling into holes with snakes, but nothing else.
Snake's Revenge. I think there were a lot of tanks to crawl under, and some keycards, but that's it
Startropics: A yoyo weapon, and a puzzle involving a piano are all that I can remember. The sad thing is, I do know that I really loved this game.
Startropics 2: I remember even less about the sequel. I can picture one portion of the overworld with a mountain, but even that is hazy.
Tiny Toons: I remember a roller coaster level, and that's it
Zelda II: I only remember the random encounters for going in grass.
Even more recently (since 2010/the introduction of trophies), my memory doesn't fair that much better;
Bastion: I hate that I can't remember anything about this one, because I know I loved it. I only recall that it has a narrator that talks throughout the entire game. I do have one of the songs on my regular playlist though, so there is that.
Dragon's Crown: I know I played as the archer, but nothing else.
Dust: An Elysian Tale. There is a freeza-looking boss at the start, and it's a metroidvania. Can't remember the story, or even what abilities you get.
Dyscourse: So, according to Steam, not only did I beat this game, I got 100% achievements in it. I'm not calling Steam a liar, but I have 0 memory of this one. The art looks familiar, but that is the extent of my memory
Kirby's Epic Yarn: You are yarn. Yea, that's all I got
Mini Ninjas. I literally recorded a youtube series on this game, and I couldn't tell you what happened. There might have been a level where you had to escape an avalanche?
All of the Prince of Persia games. I know most of them were supposed to be connected in some way, but I can't remember anything about them. At best, one of the games had a "hub" like area that a bunch of puzzles branched off of, and then lead back to.
Stories of Bethem: I know I enjoyed it. In fact, I remember constantly recommending it to people looking for zelda-likes in the CE Summer/winter events. But I just don't remember a single thing about it anymore.
Valdis Story: I remember that it is a metroidvania, and that's it. There might be a subway somewhere in it?
Yonder: The Cloud Catcher. I know I got a platinum in it, and I remember being frustrated at the grind to do so, but I don't remember what I was trying to farm/catch to achieve it.
There are plenty of others too, but at least with most of them, I can vaguely recall a final boss/encounter.
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https://i.imgur.com/MUJCZY9.png My Personal Backlog (I might have a problem) - https://i.imgur.com/CGp3x5f.png