In most areas of the game, there are various Pokémon that don't appear in the Pokédex that will appear in the wild. You get the first taste of this in Viridian Forest where a trainer tells you that they were told a Bulbasaur dwells in the forest. These are special rare spawns of Pokémon and are mostly Pokémon you cannot normally catch in the wild such as Starters, Hitmonchan/Hitmonlee and Lapras.
As they are rare, they are outside the general encounter tables and so the chances for them to spawn is low. However, there are ways of improving this. First of which is to use Lure, Super Lure or Max Lure items. You can also increase the spawn chances by amassing a massive Catch Combo. This can carry over to multiple routes but does end when you capture a Pokémon that wasn't the focus of the catch combo.
|Rare Spawns - Legendary Pokémon|
After beating the game and catching the Legendary Birds, the Legendary Birds will have a chance of appearing in the Sky as Rare Spawns. To improve odds, use a Lure and have a Catch Combo of 31 or more coming. They are incredibly rare so it may be a long way.
List of Pokémon Available As Rare Spawns