Missingno. or 'M'

Probably the most popularly known glitch, lots of people know it exists but probably not why it happens

How to Perform:

• Be able to use both Fly and Surf, and have visited Cinnabar Island already
• Talk to the Old Man in Viridian City and watch his "how to catch a Pokémon" tutorial
• Fly to Cinnabar Island and surf along the east coast

What it does:

• Changes the encounter table so you run into impossibly high-level "normal" Pokémon
  • ... and several not-so-normal ones, like Missingno.
• Modifies the quantity of the 6th item in your items list to either 128 or 255

The tens-digit is trying to represent a number in base-16 but is just trying to use the sprite data a few blocks after '9' instead of the letter 'F'

Why it happens:

In short: the game reads memory it shouldn't and interprets it as valid data anyhow.

• Visiting the Old Man is important because the game writes the player's name onto the stack for temporary storage and overwrites your name with "OLD MAN"
  • When finished, the game reads from the top of the stack and replaces "OLD MAN" with your name again, but doesn't change the stack

• Cinnabar Island is unique in that it's possible to encounter Pokémon on the east coast, but doesn't have an encounter table native to the area
  • When entering a new area, the encounter table read from some table and put into active memory. Normally, this is the previous area you were in, so it's not an issue...
  • ...but if you just came from Viridian City with your character's name on the top of the stack instead, the game reads your name as if it were encounter data

• Therefore, what you encounter using this glitch depends on the name you input at the beginning of the game
• Or more specifically, the characters in spots 3, 5, and 7 of your name determine which Pokémon show up

A: Golduck
B: Hypno
C: Golbat
D: Mewtwo 
E: Snorlax
F: Magikarp
G: Missingno.
H: Missingno.
I: Muk
J: Missingno.
K: Kingler
L: Cloyster
M: Missingno. 
N: Electrode
O: Clefable
P: Weezing
Q: Persian
R: Marowak
S: Missingno.
T: Haunter
U: Abra

V: Alakazam
W: Pidgeotto
X: Pidgeot
Y: Starmie
Z: Bulbasaur 
a: Missingno.
b: Missingno.
c: Missingno.
d: Ponyta
e: Rapidash
f: Rattata
g: Raticate
h: Nidorino
i: Nidorina
j: Geodude
k: Porygon
l: Aerodactyl
m: Missingno.
n: Magnemite
o: Missingno.
p: Missingno.

q: Charmander 
r: Squirtle 
s: Charmeleon
t: Wartortle
u: Charizard
v: Missingno.
w: Missingno. (KABUTOPS FOSSIL)
x: Missingno. (AERODACTYL FOSSIL)
y: Missingno. (GHOST)
z: Oddish 

• Also, the item count part of the glitch occurs due to some unintended interactions between the Pokédex and the item list
• The Pokédex stores one of 3 values for a Pokémon:
  • not seen, seen, caught
• This table is only 151 bytes long, but the index for the 'M' variant of Missingno extends past this
• Game Boy hardware doesn't have support for array guards, so ... an array is really just a pointer and doesn't 'know' its max length

#define NOT_SEEN = 0;
#define SEEN = 128;
#define CAUGHT = 255;

byte pokedex_table[151];
byte item_list[41];
byte missingno_pokedex_index = //some byte that's definitely greater than 151
pokedex_table[missingno_pokedex_index] = SEEN or CAUGHT;

Glitch 2: Catch Mew without cheating

No Gameshark, no external devices, nothing except natural in-game input

How to Perform:

Not just for Mew, and not intended by the developers

• Have at least one trainer with a maximum "sight" distance equal to the length of the screen not fought yet and some way to instantly travel (Escape Rope, Dig, Teleport, Fly)
  • For Mew: Gambler on Route 8, youngster on Route 25
• Has some margin of error - save beforehand to easily retry
• Step towards this trainer so they will attempt to battle you as soon as you step
• There will be one frame where you can pause the menu -- use this chance to travel before the fight starts

• After successfully cancelling the fight, run into grass
  • Doesn't matter where -- we're doing more "override the encounter table" shenanigans
• A very specific Pokémon should show up!
  • Which one depends on which trainer you used for this glitch

Why it happens:

• We're able to pause the game for one frame while the trainer gets loaded onto the screen
  • The trainer always faces south, then turns, creating an extra frame of delay in this case
• Encounter data is loaded for the fight to begin, depending on the trainer
  • The Pokémon itself is dictated by the Special stat Pokémon in the trainer's last slot
    • Certain trainers have Special stats that generate Mew
  • The level depends on the modifier on the attack stat (starts at 7, ranges from 1 to 13, modified with buff/debuff moves like Growl or Swords Dance)

More than 151 again

• What happens if the Special stat picks something outside of the normal range of 1-151?
• Same thing as Missingno, just a different method
  • With even more possibilities!

http://bulbapedia.bulbagarden.net/wiki/List_of_glitch_Pok%C3%A9mon