Mew from Early Pokemon Games
Only given out to select players at promotional events, accessing Mew in Pokemon Red and Blue became the center of perhaps the most rampant internet rumors of all time. I tried getting to level 100 then sending Squirtle out on the S.S. Anne to get strength, then hitting up, down, up, down, left, right, B, A, select, start, but it never moved the truck Mew was supposedly hiding under. It did, however, summon Cthulu in real life, which totally got me grounded. Eventually, a glitch was found to access the character.