My first shiny ever was the Red Gyarados, but I've had several others.
Crystal: Cleffa, Elekid, Pichu, Stantler
Ruby: Swablu (Which I found last night, actually.)
Sapphire: Carvanha/Sharpedo (The Sharpedo's pink. ><)
Emerald: Linoone
FireRed: Squirtle
Diamond: Shinx, Ralts
Platinum: Bidoof (><;;, Starly
I must be lucky or unlucky because a few of these shinies are crap pokemon. Like Bidoof...