Pokémon Crystal - Examining the "out of bounds" glitches

Gen II is notorious for its weird out of bounds glitches. Walking out of bounds causes many different effects, seemingly at random. How does OOB work in Gen II, and why do these effects happen? Let's investigate!
In order to make the game ignore all map connections, patch RO25:6877 (CheckTileEvent+0x0003) to 0x18 (hex edit the ROM and change byte at offset $96877 to 0x18).
About out of bounds in Gen I games: • Pokémon R/B/Y: What's ...