Cowboy BeBop at His Computer: For months prior to the official release of the game promotional materials referred to the Pokémon Marill as "Pikablu" likely due to its mouse-like appearance, the zig-zag tail that resembled Pikachu's lightning bolt tail and... well, the fact that it was blue. Marill was never officially referred to by this name at any point, not even during the planning stages. Despite this the misnaming was so prevalent that even Topps used it in the Pokémon: The First MovieTrading Cards.
God Never Said That: Marill is very frequently treated as a Pikaclone by the fandom. While the parallels are there, Game Freak has never officially promoted Marill's line in that capacity, and the association is a leftover from the old "Pikablu" rumors.
Silver (the Rival, not the game) is sometimes jokingly referred to as ???.
The three games are collectively referred to as GSC and the Metal Generation.
Serendipity Writes the Plot: The limited space of Game Boy Color cartridges is more than likely the reason that many buildings and dungeons in Kanto have been scaled down or became inaccessible due to various plot reasons in Kanto. For example, Cinnabar Island's volcano erupted and destroyed almost everything, Fuchsia City & Cerulean City's shared music was replaced with that of Celadon City and Viridian City, respectively, and most of Silph Co. isn't open to the public. HeartGold and SoulSilver restores most of the areas and their music, though Cinnabar Island is still destroyed and the Fuchsia City Safari Zone has been with replaced with the Pal Park.
In an early build of the game, the name of New Bark Town was going to be Silent Hills.
Each town and city in Johto has an alternate map in the games' ROM with different layouts than the the final product. There is also a map for a town or city located in the Lake of Rage, complete with its own Gym.
Updated maps for Cinnabar Island's Pokémon Lab are in the data (though they have no event data), indicating that the island was originally going to return unchanged.
There's an unused script for an encounter with a Level 40 Entei, implying that it (and possibly Raikou and Suicune) was originally intended to be found in a static spot instead of randomly roaming around Johto.
Pre-release material promised a skateboard item (separate from the bike) that would be allow access to new areas.
An image◊ from the magazine MicroGroup Game Review shows unused designs for 2 Pokémon; a turtle that resembles Tirtouga from Pokémon Black and White and what can only be described as a Hitmontop and Clefairy hybrid. It also shows that Tyranitar was going to be brown instead of green.
A string of text in the ROM suggests that the Honey Tree mechanic that debuts in Pokémon Diamond and Pearl was originally intended for these games.
Staryu and Starmie may have been originally intended to have genders, as Staryu has Egg Moves programmed for it and both are able to be taught Attract (a move that only works if the user and target have opposite genders) in these games only.
In an "Iwata Asks" interview, it was confirmed that Gold & Silver were intended to be the last installments in the series, as the developers felt that they were too much of a Tough Act to Follow.
The battle with Red was originally planned to pull data fromPokémon Red and Blue so that Red would use the Pokémon the player used completed the original game with. This proved too difficult to implement with the technology available at the time, so the default option of the three previous starters and the plot-relevant Pokémon were used instead.