Wow, there are so many. Here are a few specifically for Pokemon Red, Blue, and Yellow:
Missingno
Missingo is glitch shared in Pokémon Red , Blue and Yellow. It is a dual-type Bird/Normal glitch. There are actually different forms of missingno. First are the Red and Blue noram forms, whcich look like this:
Next, is the Y form which is this
The Y form is dual typed normal/normal.
Missingno also has a Kabutops fossil form, Aerodactyl fossil form and Ghost form. To catch Missigno you must make sure your name is Ash. Talk to the old man in Viridian City, and tell him you are not in a hurry(choose "no"). After, fly to Cinnabar Island and surf along the coastline. You will find a MissingNo or "M". Tbh, it's kind of creepy at first.
Mew is under the Truck
The was probably he most famous rumor on how to get Mew back in the day. Regardless it was only a rumor and did
not work. When you're in Vermilion City, you must trade with a friend without talking to the captain of the S.S. Anne, thus preventing the ship from leaving. Continue on with the game until you get HM03 (Surf) and HM04 (Strength). Return to the S.S. Anne and surf to a little area to the right. You will see a truck (this part is true). The speculation is that you'll get Mew if you use Strength to mpve the truck.
Level 49 Magikarp
First, you must put a Magikarp in the daycare without letting it get any experience points or items used on it. Then, run around until it gets to level 49 (this can get annoying). Retrieve the Magikarp from the daycare lady and level it up once more with a Rare Candy. Instead of evolving into Gyarados, it'll evolve into Mew!
Bill' Secret Garden
Supposedly there is a way to get into Bill's "secret" garden. The first thing you have to do is get a starter pokemon play the game until you are allowed to trade, trade that to another game, then repeat to get the other two. Then trade them all back so you have 1 bulbausar, 1 charmander, and 1 squirtle. Then you play the game until you get to the electric plant, stopping those three characters from evolving so they stay in their stage 1. In the electric plant you capture elctrobuzz and go directly to Bill's house and avoid all the trainers and run from all battles. Move Electabuzz to your leader and have the 3 others following and 2 empty spaces.
Then you go into Bill's house and go to the back wall and supposedly hit A and a door appears after a message saying, the wall sounds hollow. Go through the door and Bill's Garden is there with all the charmander's, bulbusar's, and squirtle's you want. Then in the back of the garden there's a rock and when you touch it, mew comes out and attacks you, battle, capture and you have mew. then you have to get out of the garden and save right after you leave Bill's house or mew dies. The ending of this one didn't even make much sense.
Aside that, there are many more rumors from other games such Pokegods, Pikablu, Hidden cities and more. There are always new rumors and creepypastas which enter the Pokemon world on a weekly basis. Many are interesting to read while most are just plain dumb and ridiculous.