Is that Mew under the truck?
My favourite entry in the Pokémon series is by far Gold and Silver (and the refined perfection of their remakes, HeartGold and SoulSilver), the second generation. Everything about the game—the region, the towns, the exclusive monsters to catch, the gym leaders, the music, the addition of a day and night cycle, the badass Team Rocket scheme, the tunable radio, the fact that you can explore the entire Kanto region all over again after beating the game—just came together so perfectly, creating what was for me the ultimate Pokémon experience.
See, back in those early days of the franchise, rumours and hype were abundant; the internet was rife with the latest hoaxes about new Pokémon details, creatures, and how to catch them. When the first announcements of a true sequel to the Red and Blue Versions were made, everyone jumped onto any and all articles were released in Japanese magazines, regardless of their ability to read any of the information. As it turned out, Marill was one of the first new Pokémon to be revealed. Without knowing how to read its name, some genius kid assumed the creature’s beady eyes and a zigzag tail unquestionably equaled a direct relation to Pikachu. Within weeks, every Internet forum was abuzz with the news of this upcoming “Pikablu”.

This went on for months, even long after the first movie had hit American cinemas, in which Marril was shown in the opening short complete with a full Pokédex entry. It even spread so far that the Topps trading cards based on the first movie showed the Pokémon as Pikablu – evidently the designer and/or PR working for Topps at the time preferred to fact check by searching AltaVista (or whatever everyone used back then) rather than contacting Nintendo itself.
Let's go farther back in Poké-history—specifically, the highly coveted Mew from Red, Blue and Yellow, and the illegitimate ways to capture it without attending the official Mew giveaway tours.

Every kid and his dog had some kind of wacky theory involving a stupidly lengthy and complicated method to catch this thing. Many of them centered on the mysterious truck parked near the S.S. Anne for a short portion of the game. Some rumours involved finding a secret room in the Cinnibar Island cloning lab. Others made ludicrous demands to waste players' time by claiming that you need to catch 150 Pikachus. Needless to say, these stories were complete and utter bunk... except one. One player under the screen name of TheScythe actually discovered a working way to capture a Mew, or any Pokémon for that matter, in the wild, and posted detailed instructions on GameFaqs. The ironic thing was that everyone was so sick to death of hearing these crazy stories that nobody believed a word of it until much later—around 2003—when most people had stopped playing the original games.
While we're talking about glitches that worked, I'll take a brief moment to fondly remember my MissingNo, caught during a time when my obsessive desire to catch 'em all heavily outweighed my rational judgment. My Hall of Fame was never the same again, but it was such fun catching you, MissingNo. I hope you're happily corrupting data wherever you are now.

Mew 3D picture credit goes to Drew108 - http://drew108.deviantart.com/