grow to level 100 instantly
You may already know that in red/blue it is possible to catch level 100 or even level 245 pokémon off the coast of Cinnabar Island. This depends on the character's name, and can be done on the red and blue versions but not yellow. Another technique is to use rare candies which can be duplicated by encountering 'M.
Recently, a more sophisticated technique was discovered. It first requires understanding the Mew glitch, so if you haven't already managed to catch a Mew please go back and read that section. That said, the following is a description of the level 100 growth technique written by Mr. Pwnage:
For a long time, it was wondered where the number 7 for the enemy level comes from. Since the first week of the discovery, levels such as 8 or 9 were known to happen, but their cause was a mystery. What's a variable with a default value of 7? The answer, as it turns out, is stat modifier variables. The range of -6 to +6 is represented using the numbers 1-13. And as it was recently uncovered, the opponent's Attack stat modifier is what's been controlling the level, and since the mindset of performing FCBM (which stands for fight-cancelled battle manipulation, the term I've given to describe this so-called "Trainer/Fly" glitch) usually just wants you to dispatch the Pokemon used to manipulate the fight quickly, Attack modifiers rarely got a chance to matter, leading to the belief that level 7 is just what "happened".
So you can find your Mew, or whatever else you want, at a level from 1-13 (though levels 8 and up will require that the enemy has Swords Dance or something similar). As it turns out, level 1 (and only level 1) is the key here. There are four different formulas determining how EXP leads to level growth, and three of them are just scalars applied to L^3. The fourth one is more complex, 1.2L^3 - 15L^2 + 100L - 140. The first few levels for these "Fading" schedule Pokemon require very few EXP--what's interesting is the result of that formula for levels less than 2. No Pokemon was ever supposed to exist below level 2, so it was thought that the hole in this formula didn't matter. But now that you've seen that you can catch a Pokemon at level 1, it becomes relevant. A Fading-schedule Pokemon at level 0 has -140 EXP, and at level 1 it has -54. The game expects EXP to be 24 bits unsigned, so treats these signed values as the unsigned 16777076 and 16777162, respectively. Indeed, if you check the information on your level-1 Mew, you'll find that its EXP Points are listed as a blank non-character tile followed by 777162.
Because the game has no reason to believe experience should ever go negative, that level-1 Mew is treated as if it really does have over 16 million EXP, which would be enough for level 245. If you can get the game to recalculate level on that, it'll be considered as 245 and then immediately be brought down to 100 like all Pokemon of level 101+ are upon participating in battle. But as I just tested, this check is made after the experience is awarded, and if you get enough to wrap around to 0 or a bit more, this won't come into play and Mew will be treated like just another low-level Pokemon. You'll need to get 53 or fewer experience awarded to Mew in order to trigger the event.
In layman's terms, here is how you do it:
|Set up the so-called Mew glitch with plans to catch a Bulbasaur, Ivysaur, Venusaur, Charmander, Charmeleon, Charizard, Squirtle, Wartortle, Blastoise, Pidgey, Pidgeotto, Pidgeot, Nidoran♀, Nidorina, Nidoqueen, Nidoran♂, Nidorino, Nidoking, Oddish, Gloom, Vileplume, Bellsprout, Poliwag, Poliwhirl, Poliwrath, Abra, Kadabra, Alakazam, Machop, Machoke, Machamp, Bellsprout, Weepinbell, Victreebell, Geodude, Graveler, Golem, Gastly, Haunter, Gengar, Dratini, Dragonair, Dragonite, or Mew.|
|In the battle before the catch, use Growl or another attack-reducing move at least six times to minimize your opponent's attack stat.|
|When you get to the next random battle, your new pokémon will pop up, but this time it will be level 1. Catch it and save your game, just in case you miscalculate on the next steps.|
|Encounter a fairly weak pokémon in a random battle, and use the switch technique to gain some experience for your level 1 pokémon.|
|Make sure your level 1 pokémon gains 53 experience points or less.|
|Your pokémon will immediately grow to level 100.|