What is the objectively worst game you've finished, not because of outright stubbornness, losing a bet, or simply hate-playing it, but rather because you somehow found joy underneath all of the rubbish?
In my case that game would be the Sega CD's pack-in game, Sewer Shark. No doubt much of the reason was the novelty of the FMV-game medium to me on a brand-new system. However, teenage me also enjoyed the over the top cheesy script and presentation layered on top of a rather bland rail shooter. To be fair, if the price of getting to see annoying bermuda-shorts boss guy get his comeuppance was to shoot another several dozen sewer rats, then that was a price I was willing to pay.
Heiankyo Alien (GameBoy) - a game about invading aliens on a maze-like town map. You fight them off by digging holes, waiting for them to fall in, and then burying them alive before they can climb out. Ludicrous, but also oddly entertaining.
Crimson Sea (Xbox) - do you like shooting endless amounts of bugs with terribly repetitive gameplay? Not so much? Well, do you like massive cleavage? Then we've got the game for you! To be fair, the bug blasting was sometimes ok in a Dynasty-Warriors "zone out" sense (both game series by Koei), but I'm ashamed to admit that early 20's me became aware of the Crimson Sea mostly for the second reason stated above.