I've played some dodgy games for a while, usually completing them, but wouldn't exactly say I love them.  Most of these are really old games.
Raptor - a shoot-em-up I used to play when I was like 6.  Managed to get the whole game recently and finished it.
Blake Stone - I played this for a while recently, again because I played it when I was young.  Really a crappy old FPS which wasn't quite as good as Doom.
.. insert other old games I can't think of right now here ..
Random dating sims - people were playing SimGirl at school in Year 9 (later found out it was a H-game, so funny they were playing it at school) - kinda looked interesting so I tried it myself.  And I did actually persist with all that repetitious "training" you have to do.  Have also tried Love Hina SimDate, which is pretty much just as stupid/annoying (but then, I actually bothered to finish it, so go figure).
Various SNES games I've just fooled around with, like Parodius (kinda funny; apparently parody of Gradius) and Miracle Girls (a 2D Mario like game, except you're in a world with all these flowers, you're enemies are these bunnies and you "shoot" candy or something which freezes your enemy for a short while; your super-attack shoots candy everywhere, lol).

Have played Mind Arms - some free Jap-style fighting game.  Also Magical Battle Arena.  Not that great a game, but fun to bash around the keyboard a bit and watch dazzling effects.
Then of course, there's the crappy games you play over with friends and stuff and everyone laughs at the thing.