The first game that comes to mind is Deadly Towers. Oh, Deadly Towers, how I both hate you and love you so much. (Well "love" is a strong word. I "like" you and I also hate your guts.) I had about 50 NES games. Most of them I'd play for a couple of weeks or so and then beat. Then I'd have a lull until I had money to get another game, so I'd reach over and pop in Deadly Towers.
This game is so stupidly, unfairly hard. A typical enemy is a bouncy ball that takes like 20 hits to kill. You can go exploring, but then you find an invisible entrance to a dungeon where the enemies fly across the screen with super speed and then knock you into another room with another group of equally tough enemies. Even if you can survive, the dungeons are huge and every room looks the same. But you have to navigate these dungeons so that you can gradually buy better equipment.
On and off for over 2 years, I would play Deadly Towers. I'd put it in, get maybe one upgrade after hours of trying, then I'd give up in frustration. But I always saved my password. Gradually, I upgraded my gear. Finally after 2+ years I finally managed to beat the game. I finally beat the game that was by far the hardest game I'd ever played. I felt such a sense of accomplishment even though the game sucks.
Fuck you Deadly Towers! I made you my bitch!