Weirdest rumor I've ever heard was the one about Chronomew.
Basically, it entailed going to Cinnabar Island and Surfing up and down the coast using the Itemfinder. Eventually, the Itemfinder will beep, and when it does, you're supposed to use Dig (yes, Dig) on that patch of water (yes) to get an item called a Mist Stone. If you used this stone on a Mew, it would evolve into a secret Pokemon called Chronomew.
Second weirdest one had to be the one where, if you battled the E4 100 times, Oak will take you into the Hall of Fame and tell you that he's tired of recording you. Then, he'll leave, and you'd be allowed to roam the room. Eventually, you could find a door that leads to a secret town where you can battle your rival (who is inexplicably the Gym Leader there) and buy special Poke Balls that allow you to steal Pokemon from trainers.
Oh, RBY and your awesome rumors.