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Ascended Glitch and Good Bad Bugs has quite a few examples.
TV Tropes's No. 1 bread themed lesbian. she/her, fae/faerMy first thought was .hack, except if I remember right that was viruses, not glitches.
How about ROM CHECK FAIL (which is a game about a mashup of different games, in which the graphics, player character, and enemies randomly switch among different games)? There's also a flash game I have played before, though I don't remember the name, in which the main gimmick was that a bunch of games in a compilation were mixing together, and in each level you could cross lines between each world and switch the gameplay to have different ways of moving around.

Just watched Wreck-It Ralph with Vanellope using her glitch powers to win the race, and a thought crossed my mind: was there ever a videogame about glitches? A game where things that happen accidentally in other games and ruin them are acknowledged and used as a part of the game's actual mechanic? I'm not sure if such a game exists, but I can't be the first one to think of it, right?