From Bulbapedia, the community-driven Pokémon encyclopedia.

Roaming Pokémon are a type of legendary Pokémon that, instead of remaining in one place as a special event, run around the region they appear in, seemingly randomly.

In addition to their changing of routes, something that happens every time the player enters or leaves a separate location, they also, on the first turn of battle, will attempt to flee. The only way to prevent this is to use a move such as Mean Look or have the Pokémon sent out have an ability such as Shadow Tag.

Most often, a trainer can use his or her Pokédex to check the ever-changing location of their target. However, in Sinnoh, the Pokétch's Marking Map app serves this purpose so that the player has no need to change through a multitude of screens, as was the case in other regions.

Roaming Pokémon appear in every game released starting with Generation II.

Region	Pokémon
Kanto*	Raikou*		Entei*		Suicune*
Johto	Raikou		Entei		Suicune*
Hoenn	Latias*			Latios*
Sinnoh	Mesprit			Cresselia

Game locations of Legendary Pokémon
Articuno	Zapdos	Moltres	Mewtwo	Mew	Celebi	Jirachi
Seafoam Islands	Power Plant	Victory Road*	Cerulean Cave	Faraway Island*	Ilex Forest*	None*
		Mt. Ember*
Raikou	Entei	Suicune	Lugia	Ho-Oh	Latias	Latios
roaming Johto*		roaming Johto*	Whirl Islands*	Tin Tower*	roaming Hoenn*
		Tin Tower*
roaming Kanto*			Navel Rock**		Southern Island**
Regirock	Regice	Registeel	Kyogre	Groudon	Rayquaza	Deoxys
Desert Ruins	Island Cave	Ancient Tomb	Cave of Origin*		Sky Pillar	Birth Island*
			Marine Cave*	Terra Cave*
Uxie	Mesprit	Azelf	Dialga	Palkia	Heatran	Regigigas
Lake Acuity	Lake Verity* roaming Sinnoh	Lake Valor	Spear Pillar		Stark Mountain	Snowpoint Temple*
Giratina	Cresselia	Phione	Manaphy	Darkrai	Shaymin	Arceus
Turnback Cave	Fullmoon Island* roaming Sinnoh	breed Manaphy	Egg*	Newmoon Island*	Flower Paradise*	Hall of Origin*