Roaming Pokémon

Roaming Pokémon are rare Pokémon that can be found randomly while on routes. Each region has a set of Roaming Pokémon that can be caught. So far, only Mew and Manaphy have no requirements to appear.

Odds
The chance to encounter a roaming Pokémon is 1/8192 for the first route of a region, and increases linearly up to 1/4096 for the last route of a region. "first" and "last" here just being the route number, not necessarily the order you reach the route

Kanto
No current requirement.
 * Mew

Johto
Complete the Burned Tower dungeon.
 * Raikou
 * Entei
 * Suicune

Hoenn
Become the Hoenn champion.
 * Latios
 * Latias
 * Jirachi

Sinnoh
No current requirement. Complete Fullmoon Island Complete Lake Verity
 * Manaphy
 * Cresselia
 * Mesprit