In Generation I
In Pokémon Red, Blue, and Yellow, in order to fish at all, not only must the player be facing a water tile (sub-tile 0x14 and specific to the tileset) but certain tilesets (W_CURMAPTILESET; D367 in Red/Blue and D366 in Yellow) will forbid fishing (and Surfing) anyway.
On non-water tilesets, attempting to fish will bring up the message "OAK: (PLAYER)! This isn't the time to use that!" even if the player uses glitches to face the equivalent 'water tile' pertaining to that tileset.
The tileset (water tilesets in the disassembly projects) must be one of the following:
OVERWORLD FOREST DOJO GYM SHIP SHIP_PORT CAVERN FACILITY PLATEAU
However, the player can use the expanded inventory to change the value of W_CURMAPTILESET without having to reload the tileset itself; changing it to a 'good' tileset such as 00 (OVERWORLD) will then allow fishing.
Encounters using the Rod
Provided that the tileset (or value of W_CURMAPTILESET) matches one of the 'good' tilesets above, Old Rod encounters will still always give a Level 5 Magikarp with a 100% chance, Good Rood encounters will bring up a random fish Pokémon (either a Level 10 Goldeen or Level 10 Poliwag) or give the text "Not even a nibble!" and this is not specific to the map (see here).
Unlike the other rods, Super Rod encounters do have encounters specific to the maps included with those encounter slots (furthermore the versions Red/Blue or Yellow, which have there own unique Super Rod Pokémon lists), so if one considers valid source map Glitch City to count as "glitch maps", the hooked Pokémon that appear will be taken from the original map. For example, a Pallet Town Glitch City in Pokémon Yellow would have possible Super Rod encounters (provided there was a bite) as Level 10 Staryu, Level 10 Tentacool, Level 5 Staryu, or Level 20 Tentacool, and in Pokémon Red/Blue the possible encounters for a Pallet Town Glitch City are Level 15 Tentacool and Level 15 Poliwag.
In maps which do not have Super Rod encounters (such as Cerulean City Gym or Lorelei's Elite Four room), fishing with a Super Rod always returns "Looks like there's nothing here." However, if the length of the Super Rod encounter slot data is extended using Game Genie or an invalid fishing group is accessed, there are artificial glitch encounter slots beyond the last slot (for Red/Blue these are the groups beyond group 10 (Fuschia City), for Yellow the structure is slightly different and glitch fish would relate to the slots beyond 31: Cerulean Cave B1F). As Rod encounters work by writing to W_CUROPPONENT (D059 in Red/Blue and D058 in Yellow), fishing for Trainers/glitch Trainers is also theoretically possible.
Other "hooked" Pokémon
If bit 0x0 of D05F (D05E in Yellow) is set before the start of a wild battle, that Pokémon will be "hooked" even if no rod was used to catch it. This applies to glitches which corrupt D05F/D05E such as unterminated name glitch items (usually always a hooked Metapod in non-Japanese versions because the species is taken from the 0x7C menu-tile that typically never changes during the glitch), or a path buffer overflow.