Major glitches of the Pokémon series
Arbitrary code execution 
0x1500 control code arbitrary code execution (Crystal) | Cart-swap arbitrary code execution | Generation I custom map script pointer | Generation I invalid meta-map scripts | Generation I item ("8F", "ws m", "-g m", "5かい", "てへ" etc.) | Generation I move ("-", "TM42") | Generation I Trainer escape glitch text boxes | Generation II bad clone | Generation II Burned Tower Silver | Japanese Crystal Pokémon Communication Center SRAM glitches | Coin Case glitch | Generation II glitch Pokédex sortings | Pikachu off-screen glitch ACE | OAM DMA hijacking | Pikachu glitch emote | Generation III glitch Pokémon summary | Generation III glitch move animation) | Remote code execution | TM/HMs outside of the TM/HM pocket | ZZAZZ glitch Trainer FC
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No further extensions 
Cloning | Item duplication glitch (Generation I) | Pokémon merge glitch ("Q Glitch", Generation I) | Time Capsule exploit | Bug-Catching Contest data copy glitch (Generation II, Japan only) | Berry glitch | Battle Tower Lati@s glitch (Generation III) | (Mimic) Transform Rage glitch (Generation IV)
Transform held item glitch (Generation IV, Japan only) | Mimic glitch (Generation IV, Japan only)
[hr]
Buffer overflow techniques 
99 item stack glitch | LOL glitch | Rival LOL glitch | Instant LOL glitch | RAM LOL glitch | Out of bounds LOL glitch | blockoobLG | Instant encounter infinite chain glitch | LGFly | Super Glitch (Generation I) | Party remaining HP glitch | Super Glitch (Generation III) | Text pointer manipulation mart buffer overflow glitch | CoolTrainer♀-type move | Double distort CoolTrainer♀ corruption | Yami Shop glitch | Party Pokémon box data shift glitch | Unterminated name glitch item instant encounter (Japanese Red/Green)
[hr]
Item stack duplication glitch (Generation I) 
Generation I expanded items pack (Glitch Rocket HQ maps, Map FE (English and non-English European Yellow) | Map script pointer manipulation (arbitrary code execution | Map script pointer item ball manipulation) | Text pointer manipulation (arbitrary code execution | Item ball manipulation | Mart buffer overflow) | Trainerless instant encounter glitch
[hr]
Bad clone glitch (Generation II) 
????? party overloading (Type 0xD0 move glitch | ????? map corruption | Celebi trick | Celebi Egg trick | Shiny Celebi trick | Glitch move map corruption | Overloaded party map corruption | Glitch Unown (Glitch Unown map corruption) | Duplicate key items glitch (Infinite items and item creation, Expanded Balls pocket (Wrong pocket TM/HMs, Glitch Pokédex categories))
[hr]
Closed menu Select glitches (Japanese Red/Green) 
Dokokashira door glitch (International) | Fossil conversion glitch (international) | Second type glitch | Skip to Level 100 glitch | Trainer mutation glitch | Walk through walls (International) | Lift glitch | Badge describer glitch
[hr]
Pomeg glitch (Generation III) 
Pomeg data corruption glitch ("Glitzer Popping") | Charm glitch
[hr]
Voiding (Generation IV) 
Tweaking
Broken escalator glitch (Japan only) | Elite Four door glitch (Japan only)
[hr]
2x2 block encounter glitches (Generation I) 
Left-facing shore tile glitch (in-game trade shore encounter trick, Old man trick, Trade link up shore encounter trick, Fight Safari Zone Pokémon trick) | Viridian Forest no encounter grass tiles glitch
[hr]
Glitch City 
Safari Zone exit glitch | RAM manipulation | Out of bounds Glitch City (Generation II) | Slowpoke Well out of bounds corruption (French Gold/Silver/Crystal)
[hr]
Large storage box byte shift glitch 
Storage box remaining HP glitch | Generation I max stat trick
[hr]
Pikachu off-screen glitch 
Trainer corruption glitch
[hr]
SRAM glitches 
Generation I save corruption | 255 Pokémon glitch | Expanded party encounter table manipulation (Generation I) | Send party Pokémon to a new game (Generation I) | Generation II save corruption | Mailbox glitches | Mystery Gift item corruption | Trainer House glitches
[hr]
Trainer escape glitch 
Death-warp | Ditto trick | Experience underflow glitch | Mew trick | Text box ID matching | Meta-map script activation
[hr]
Walk through walls 
Ledge method | Museum guy method | Rival's effect | Select glitch method (International Select glitch method), Brock Through Walls
[hr]
Surf down glitch 
Grass/rock Surfing glitch (Spanish/Italian only) (adaptions: Submerge glitch (international)) | 8 8 (0x7C) grass/rock surfing glitch (English Red/Blue))
(view, talk, edit)


0x1500 control code arbitrary code execution (Crystal) | Cart-swap arbitrary code execution | Generation I custom map script pointer | Generation I invalid meta-map scripts | Generation I item ("8F", "ws m", "-g m", "5かい", "てへ" etc.) | Generation I move ("-", "TM42") | Generation I Trainer escape glitch text boxes | Generation II bad clone | Generation II Burned Tower Silver | Japanese Crystal Pokémon Communication Center SRAM glitches | Coin Case glitch | Generation II glitch Pokédex sortings | Pikachu off-screen glitch ACE | OAM DMA hijacking | Pikachu glitch emote | Generation III glitch Pokémon summary | Generation III glitch move animation) | Remote code execution | TM/HMs outside of the TM/HM pocket | ZZAZZ glitch Trainer FC
[hr]


Cloning | Item duplication glitch (Generation I) | Pokémon merge glitch ("Q Glitch", Generation I) | Time Capsule exploit | Bug-Catching Contest data copy glitch (Generation II, Japan only) | Berry glitch | Battle Tower Lati@s glitch (Generation III) | (Mimic) Transform Rage glitch (Generation IV)
Transform held item glitch (Generation IV, Japan only) | Mimic glitch (Generation IV, Japan only)
[hr]


99 item stack glitch | LOL glitch | Rival LOL glitch | Instant LOL glitch | RAM LOL glitch | Out of bounds LOL glitch | blockoobLG | Instant encounter infinite chain glitch | LGFly | Super Glitch (Generation I) | Party remaining HP glitch | Super Glitch (Generation III) | Text pointer manipulation mart buffer overflow glitch | CoolTrainer♀-type move | Double distort CoolTrainer♀ corruption | Yami Shop glitch | Party Pokémon box data shift glitch | Unterminated name glitch item instant encounter (Japanese Red/Green)
[hr]


Generation I expanded items pack (Glitch Rocket HQ maps, Map FE (English and non-English European Yellow) | Map script pointer manipulation (arbitrary code execution | Map script pointer item ball manipulation) | Text pointer manipulation (arbitrary code execution | Item ball manipulation | Mart buffer overflow) | Trainerless instant encounter glitch
[hr]


????? party overloading (Type 0xD0 move glitch | ????? map corruption | Celebi trick | Celebi Egg trick | Shiny Celebi trick | Glitch move map corruption | Overloaded party map corruption | Glitch Unown (Glitch Unown map corruption) | Duplicate key items glitch (Infinite items and item creation, Expanded Balls pocket (Wrong pocket TM/HMs, Glitch Pokédex categories))
[hr]


Dokokashira door glitch (International) | Fossil conversion glitch (international) | Second type glitch | Skip to Level 100 glitch | Trainer mutation glitch | Walk through walls (International) | Lift glitch | Badge describer glitch
[hr]


Pomeg data corruption glitch ("Glitzer Popping") | Charm glitch
[hr]


Tweaking
Broken escalator glitch (Japan only) | Elite Four door glitch (Japan only)
[hr]


Left-facing shore tile glitch (in-game trade shore encounter trick, Old man trick, Trade link up shore encounter trick, Fight Safari Zone Pokémon trick) | Viridian Forest no encounter grass tiles glitch
[hr]


Safari Zone exit glitch | RAM manipulation | Out of bounds Glitch City (Generation II) | Slowpoke Well out of bounds corruption (French Gold/Silver/Crystal)
[hr]


Storage box remaining HP glitch | Generation I max stat trick
[hr]


Trainer corruption glitch
[hr]


Generation I save corruption | 255 Pokémon glitch | Expanded party encounter table manipulation (Generation I) | Send party Pokémon to a new game (Generation I) | Generation II save corruption | Mailbox glitches | Mystery Gift item corruption | Trainer House glitches
[hr]


Death-warp | Ditto trick | Experience underflow glitch | Mew trick | Text box ID matching | Meta-map script activation
[hr]


Ledge method | Museum guy method | Rival's effect | Select glitch method (International Select glitch method), Brock Through Walls
[hr]


Grass/rock Surfing glitch (Spanish/Italian only) (adaptions: Submerge glitch (international)) | 8 8 (0x7C) grass/rock surfing glitch (English Red/Blue))
(view, talk, edit)

An advantage to this glitch over Coin Case glitch is that it may not corrupt the stack (similar to wrong pocket TM ACE which never corrupts the stack), however it requires move 0x00 which can only be obtained by trading a Pokémon with it over from Generation I (such as "-" move Ditto with the swapping Transform moves glitch, obtaining a bad clone, or using another form of arbitrary code execution).
This glitch has been used in any% speedruns of Pokémon Gold and Silver (see here), and was researched by luckytyphlosion. ChickasaurusGL also adapted it for non-speedrunning uses.
Summary
You can execute arbitrary code by moving in a specific way in Cherrygrove City (see pictures below) and viewing move 0x00 from the move description menu in a Pokémon's summary provided the following requirements are met:
1. You have exactly four Pokémon.
1i) The first Pokémon has move 0x00 (e.g. a "CoolTrainer" Ditto).
1ii) The third Pokémon is a low level 'slide' Pokémon you caught in the wild (whether it will work is up to chance but if you find one that works it will always work, possibly the same one compatible for Coin Case ACE without bad DVs etc.)
1iii) To be safe have Pokémon 2 and 3 have the bird and tailed creature menu sprites and have no Pokémon hold an item except for Pokémon 4.
2. Pokémon 4 is a Quagsire with TM02 and Return as its first move (for box name ACE at D8C0 (box 1 character 2)) or a Quagsire with HP Up and Sleep Talk as its first move (for stored items ACE at D61A (second item quantity)).
Before you move one step up and four steps right from picture 3, save the game. Afterwards view Pokémon 1's moves from the move description menu and close it repeatedly until your code works.
Sometimes this will not execute arbitrary code. At times it is possible to get a flashing color 'disco' effect as well.
Example box name code
This box name code with many thanks to Crystal_ for the concept allows us to warp to the Bug-Catching Contest and obtain Celebi.The box names for that are as such:
Box 1: Bp'vZ'vL55
Box 2: é'r2p'vA'vF
Box 3: é!Ap'v/'v)
Box 4: é?2p'v5'vA
Box 5: 'vBéA'tp'vZ
Box 6: 'v[éx2
(x is the multiplication sign)
Technical information
Move 0x00 has a glitch type, specifically glitch type 0xD0. The source of its glitch type is 0x8350 in VRAM, hence what is or what was on the screen will affect what the game brings up as a type name; possibly with what's on the Pokémon menu affecting 0x8350[citation needed]
When we have 'good' data at 0x8350 the name of the glitch type causes memory corruption, and by making the specific movements in Cherrygrove City/meeting the party requirements the game may start to execute arbitrary code on attempts, seemingly at random.
If by chance the game executes E9F0 (Echo RAM for C9F0) then it will eventually come across jr c, EC68 (@EC2D) and jp c, FA9B (@EC70), which causes the game to execute FA9B (DA9B).
As DA9B is Pokémon 3's Speed DVs, we can make the data slide over to Pokémon 4. Using Quagsire, the code can be redirected to somewhere else (such as box names or stored items) where we can spell out code.
Here is the assembly code for the box name code to obtain Celebi:
xor a sub 99 sub 8b ei ei ld d,b ld (f8d3),a xor a sub 80 sub 85 ld d,b ld (80e7),a xor a sub f3 sub 9b ld d,b ld (f8e6),a xor a sub fb sub 80 ld d,b sub 81 ld (d580),a xor a sub 99 ld d,b sub 9e ld (f8f1),a ld d,b ld d,b ld d,b ld d,b