There were a couple when i was younger: the first was that “Ancient Mew” was the rarest card in the world. A kid came in with one and we all couldn’t believe it. I traded 9 base set “shinies” for it (as we used to call them) including Blastoise, Venusaur, Chansey and Alakazam, and felt like Warren Buffett.
Turns out his mom worked in a movie theatre and got the card the weekend before the movie opened. We all went to see it at the weekend, and by Monday morning we all had a copy!
Birthday Pikachu was the next “rarest card in the world” rumour.
In terms of the games, the main rumour was that catching MissingNo would brick your Gameboy. I caught it, my game started glitching, i got scared and deleted my whole save file!