I can't believe Beat Takeshi's game hasn't been mentioned. That game is legendary with how weird, obtuse and insanely difficult it is. I also really want to see someone do a first person remake of this game on Unity, GZDoom or Unreal.
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Army Men: Sarge's Heroes is also a must play for any self-respecting gaming masochist. It's an extremely glitchy and broken game. It's the kind of game where collision and hit detection are programmed according to the non-Euclidian geometries that only a human being utterly deprived of sleep and fueled by Jolt Cola and Adderall could envision after crashing out and slamming their keyboard face first.
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Shrek: Treasure Hunt is a game that drives people to alcoholism. While I am lucky enough to count myself amongst those who do not need liquid courage to function, there is something almost intangibly wrong with this game and it's poor, rushed design that is enough to drive a man to the devils drink. This collection of poorly designed mini games with an absolutely grating soundtrack will make you want to drown in Everclear.