Three staple rumors of RBY:
1.) On Yellow, beat the Elite Four 1000 times and get a free Togepi/Pikablu (NOT Marill)
2.) After you've beaten the game, surf to Cerulean Cave and walk past it until you come to the female trainer who had a Parasect (you must have battled her once.) Talk to her, then make sure you have Mewtwo sixth in your party. If you have met these conditions, you will be able to teach Mewtwo Fly. Teach it to him, then use it to fly to Viridian City. It will appear to have done nothing. Instead, walk a few steps south until you jump over the hedge, and you will be floating instead of walking. This way, you will float over the mountains if you head further south and end up in a secret place called Brick Town.
3.) Have Dratini, Dragonair, Dragonite, Articuno, Zapdos, and Moltres in your party (in that order.) Talk to Bill, and he will give you a key that opens an invisible door in the back of his house. You will enter a special cave where you can catch the pokemon Chromo Mew (there are many variations of the Chromo Mew cheat, but this is the one I've heard most commonly.)
Fell for number two many times as a n00b.