Pokemon: Ruby, Sapphire, Emerald, Firered, Leafgreen, Diamond, Pearl, Heartgold, Soulsilver, Black, White, Black 2, White 2, Alpha Sapphire, Omega Ruby, X, Y. Halo: Reach, Borderlands, Borderlands 2, Diablo 3, Paper Mario 64, Paper Mario: The Thousand Year Door, Mario and Luigi: Superstar Saga, Mario and Luigi: Dream Team, New Super Mario Bros 2, Legend of Zelda: Oracle of Seasons, Legend of Zelda: Minish Cap, Legend of Zelda: A Link to the Past, Legend of Zelda: A Link Between Worlds, World of Warcraft... And many more :D

Pokemon red, blue, green, yellow, fire red, leaf green, diamond, pearl, platinum, silver, gold, crystal, heart gold, soul silver, x, y, z. I missed a few, but all of those games have a rare gold (shiny) enemy.