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Missingno is a name shared by several glitch Pokémon in Pokémon Red, Blue, and also Yellow. The name is most commonly used to refer to a Normal/Bird-type glitch Pokémon whose sprite consists of corrupted data or a Normal/999 in Pokémon Yellow.
In the early Pokémon video games, the programmers had to use variables to refer to different Pokémon by number. Variable sizes must be powers of two. The smallest variable they were able to use was the size of one byte—that is, capable of holding any value from 0 to 255. (The next smallest size could only hold 0 to 127, which would not have been enough for all 151 Pokémon.) Because there are only 151 legitimate Pokemon in Generation I, this left 104 slots left unoccupied. 39 of these are occupied with glitches with the name of Missingno, 36 of which are occupied with the original sprite, 1 has the Kabutops fossil sprite, 1 has the Aerodactyl fossil sprite, and 1 has the Lavender Town ghost sprite.
Unlike most glitch Pokémon, whose names consist of data cobbled together from random locations, MISSINGNO.'s name is clearly a deliberately-added abbreviation of "missing number". This would seem to imply that MISSINGNO. was deliberately inserted as a placeholder or a removed beta Pokémon, albeit one with several odd quirks. The fact that 39 copies of MISSINGNO. exist (with each consuming its own "slot") would seem to support this theory.
The MISSINGNO. most commonly encountered during glitches is a Normal/Bird-type Pokémon, whose sprite is a backwards letter "L"-shaped chunk of "fuzz". Bird is a beta type that was left in the game; it functions identically to Normal. The sprite results from the game treating non-graphical data as an image. This form of MISSINGNO. almost always knows Sky Attack and Water Gun; of particular note is the fact that it knows two Water Guns. The Fossil and Ghost sprite Missingnos have the same moveset as the most recently viewed Pokemon. You can get it in the Red, Blue, and Yellow versions.
sprites from the Pewter City museum.
Other forms of MISSINGNO. use the fossilized Aerodactyl and Kabutops sprites from the Pewter City museum. The fourth form uses the sprite shown when one encounters a Ghost Pokémon in the Pokemon Tower without having the Silph Scope. These are actually separate glitch Pokémon that share a name; they can be distinguished both by their sprite and by their differing characteristics. "Fuzz" MISSINGNO., for example, uses a fixed moveset, whereas the fossil MISSINGNO.s' moves and stats change depending on the last Pokémon in one's party (among other things). The fossil MISSINGNO.s also tend to turn into RHYDON upon capture, if a player hasn't yet viewed their (empty) Pokédex entries (by, of course, capturing them).
Though they are all distinct, all known MISSINGNO. forms have several properties in common. They all share the Pokédex number 000. Encountering MISSINGNO. will increase the quantity of the sixth item in a player's inventory to above 128. (This is because the bit used to keep track of whether MISSINGNO. has been caught is also part of the byte used to track the quantity of the sixth item in a player's inventory.)
How to catch him you ask? There is a trick involving Cinnabar, but we will get to that later. First, you need to do that old glitch everyone knows called The Old Man Glitch. It allows a player to battle nearly any Pokémon they wish, depending on the characters of their name. The player should start by viewing the Old Man's Pokémon catching tutorial in Viridian City. This glitch works because of a programming oversight. When the Old Man's tutorial is displayed, the game needs to change the player's name to "OLD MAN", so that the in-game dialogue states that "OLD MAN threw a Poké Ball!". However, it would be rather unfortunate if the player's chosen name was permanently changed to "OLD MAN". Such a scenario is easily avoided, however; the game simply copies the player's chosen name to an area in memory that is not currently being used. After the tutorial, the name is copied back, replacing "OLD MAN". The player should start by viewing the Old Man's Pokémon catching tutorial in Viridian City. Immediately afterward, the player should Fly to Cinnabar Island and Surf on the east coast (the half-land half-sea tiles). They should not, at any point, swim onto a fully-water tile. Depending on the characters in the player's name, they may eventually encounter MISSINGNO. or M, another glitch pokémon. But in most instructions, it says not to catch MISSINGNO. because it will erase your save game. But this is not really true. In fact, MISSINGNO, may not delete it but cause game to freeze up and make the current save file unusable.
There was one critical mistake that the developers made, however. The Cinnabar Island map, like the maps of all cities in the game, does not contain any wild Pokémon data. However, the east coast tiles were coded to trigger wild Pokémon battles. The effect is that when the player travels from a city to Cinnabar Island directly, the wild Pokémon list is not rebuilt. This means that when sailing on Cinnabar's east coast, the player will encounter whatever wild Pokémon were available at the last area they were traveling in. (This is a useful trick for catching Safari Zone Pokémon; after exiting the Zone, fly immediately to Cinnabar and Surf on the east coast. You'll be able to battle Kangaskhans and the like on your own terms.)
In other words, he can also be encountered using a cheating device, such as a Gameshark or a Game Genie.
Here's some fast facts:
MISSINGNO.'s Japanese name (けつばん Ketsuban) means "missing number".
MISSINGNO. is the most well-known glitch Pokémon.
MISSINGNO. and 'M are the only glitch Pokémon to have Normal as a secondary type.
MISSINGNO. is known to scramble Hall of Fame data.
MISSINGNO. is the only Pokemon to know the same move (Water Gun) twice, if Smeargle learning Sketch doesn't count.
MISSINGNO. only appears in Generation I. Similar Pokemon appear in other games, though.
In the early Pokémon video games, the programmers had to use variables to refer to different Pokémon by number. Variable sizes must be powers of two. The smallest variable they were able to use was the size of one byte—that is, capable of holding any value from 0 to 255. (The next smallest size could only hold 0 to 127, which would not have been enough for all 151 Pokémon.) Because there are only 151 legitimate Pokemon in Generation I, this left 104 slots left unoccupied. 39 of these are occupied with glitches with the name of Missingno, 36 of which are occupied with the original sprite, 1 has the Kabutops fossil sprite, 1 has the Aerodactyl fossil sprite, and 1 has the Lavender Town ghost sprite.
Unlike most glitch Pokémon, whose names consist of data cobbled together from random locations, MISSINGNO.'s name is clearly a deliberately-added abbreviation of "missing number". This would seem to imply that MISSINGNO. was deliberately inserted as a placeholder or a removed beta Pokémon, albeit one with several odd quirks. The fact that 39 copies of MISSINGNO. exist (with each consuming its own "slot") would seem to support this theory.
The MISSINGNO. most commonly encountered during glitches is a Normal/Bird-type Pokémon, whose sprite is a backwards letter "L"-shaped chunk of "fuzz". Bird is a beta type that was left in the game; it functions identically to Normal. The sprite results from the game treating non-graphical data as an image. This form of MISSINGNO. almost always knows Sky Attack and Water Gun; of particular note is the fact that it knows two Water Guns. The Fossil and Ghost sprite Missingnos have the same moveset as the most recently viewed Pokemon. You can get it in the Red, Blue, and Yellow versions.
sprites from the Pewter City museum.
Other forms of MISSINGNO. use the fossilized Aerodactyl and Kabutops sprites from the Pewter City museum. The fourth form uses the sprite shown when one encounters a Ghost Pokémon in the Pokemon Tower without having the Silph Scope. These are actually separate glitch Pokémon that share a name; they can be distinguished both by their sprite and by their differing characteristics. "Fuzz" MISSINGNO., for example, uses a fixed moveset, whereas the fossil MISSINGNO.s' moves and stats change depending on the last Pokémon in one's party (among other things). The fossil MISSINGNO.s also tend to turn into RHYDON upon capture, if a player hasn't yet viewed their (empty) Pokédex entries (by, of course, capturing them).
Though they are all distinct, all known MISSINGNO. forms have several properties in common. They all share the Pokédex number 000. Encountering MISSINGNO. will increase the quantity of the sixth item in a player's inventory to above 128. (This is because the bit used to keep track of whether MISSINGNO. has been caught is also part of the byte used to track the quantity of the sixth item in a player's inventory.)
How to catch him you ask? There is a trick involving Cinnabar, but we will get to that later. First, you need to do that old glitch everyone knows called The Old Man Glitch. It allows a player to battle nearly any Pokémon they wish, depending on the characters of their name. The player should start by viewing the Old Man's Pokémon catching tutorial in Viridian City. This glitch works because of a programming oversight. When the Old Man's tutorial is displayed, the game needs to change the player's name to "OLD MAN", so that the in-game dialogue states that "OLD MAN threw a Poké Ball!". However, it would be rather unfortunate if the player's chosen name was permanently changed to "OLD MAN". Such a scenario is easily avoided, however; the game simply copies the player's chosen name to an area in memory that is not currently being used. After the tutorial, the name is copied back, replacing "OLD MAN". The player should start by viewing the Old Man's Pokémon catching tutorial in Viridian City. Immediately afterward, the player should Fly to Cinnabar Island and Surf on the east coast (the half-land half-sea tiles). They should not, at any point, swim onto a fully-water tile. Depending on the characters in the player's name, they may eventually encounter MISSINGNO. or M, another glitch pokémon. But in most instructions, it says not to catch MISSINGNO. because it will erase your save game. But this is not really true. In fact, MISSINGNO, may not delete it but cause game to freeze up and make the current save file unusable.
There was one critical mistake that the developers made, however. The Cinnabar Island map, like the maps of all cities in the game, does not contain any wild Pokémon data. However, the east coast tiles were coded to trigger wild Pokémon battles. The effect is that when the player travels from a city to Cinnabar Island directly, the wild Pokémon list is not rebuilt. This means that when sailing on Cinnabar's east coast, the player will encounter whatever wild Pokémon were available at the last area they were traveling in. (This is a useful trick for catching Safari Zone Pokémon; after exiting the Zone, fly immediately to Cinnabar and Surf on the east coast. You'll be able to battle Kangaskhans and the like on your own terms.)
In other words, he can also be encountered using a cheating device, such as a Gameshark or a Game Genie.
Here's some fast facts:
MISSINGNO.'s Japanese name (けつばん Ketsuban) means "missing number".
MISSINGNO. is the most well-known glitch Pokémon.
MISSINGNO. and 'M are the only glitch Pokémon to have Normal as a secondary type.
MISSINGNO. is known to scramble Hall of Fame data.
MISSINGNO. is the only Pokemon to know the same move (Water Gun) twice, if Smeargle learning Sketch doesn't count.
MISSINGNO. only appears in Generation I. Similar Pokemon appear in other games, though.
I would like to hear what you would like to say about Missingno.!
Are you a wizard? Do you watch me sleep? 
)