I feel like you shouldn't mention bugs, glitches, and similar without mentioning the classic bug-fest: Pokemon.
My personal favorite back in the day was turning off the game midsave at the computer, cloning your pokemon and their held items (which, if you're doing this, is almost certainly going to be masterballs, or combo-ing Toxic and Leech Seed and getting massive healing.
But of course, probably the most famous is the Cinnabar glitch pokemon, the fan favorite bird-type pokemon... Weighing in at 3500 pounds, it's everyone's favorite save corrupting tetris block...
Although if you were cool (like me) you didn't go for that ol' L block. Everybody knows the skeleton and ghost forms are where it's at! Lest we forget that Mr.No here also was capable of giving out more rare candies than Marik Ishtar on Halloween, and maybe some masterballs as well. This guy pretty much handed the rest of the game to you on a silver platter, if you were willing to risk it all for that son of a glitch