In the distant past... The Brass Tower burned in a fire. Three nameless Pokémon perished in it. A rainbow-colored Pokémon descended from the sky and resurrected them...

These legendary Pokémon are said to embody three powers... The lightning that struck the tower. The fire that burned the tower. And the rain that put out the fire...

When the legendary Pokémon appeared... They struck terror in those who saw their rise.

And...
Some even took to futile attacks. The legendary Pokémon, knowing their own power, fled, ignoring the frightened people.

(I can't get the embed to work but for now,
here's the legendary beast episode of Generations.)

Raikou, Entei, and Suicune were introduced in the second generation Pokémon games, Gold & Silver. When the player meets them in the basement of the Burned Tower in Ecruteak City, they flee and begin wandering the land. The player can then pursue them across Johto, hoping to catch them before they flee once again. In Crystal, Suicune was given a starring role (and mascot status), and no longer roamed. Instead, they were met in a succession of cutscenes, eventually allowing the player a chance to catch them in the Tin Tower.

The player meeting the beasts in Crystal. She stands before the trio in a gloomy cave.
Raikou. Resembling a tiger, they have yellow fur, with black markings and a white belly. They have a long purple mane down their back and a blue tail, shaped like a lightning bolt. The crest on their face is black on the forehead, pointed like cat ears, and blue spikes resembling whiskers. They have long fangs like a sabretooth.

Raikou

Thunder Pokémon

Height: 6ft 03in
Weight: 392.4lbs

This rough Pokémon stores energy in its body, then sweeps across the land, shooting off electricity

Entei. Resembling a stocky lion or a large dog, they have long brown fur, cream colored on their chest. They have a smoke-like mane down their back, spiky grey ridges rise on either side of the mane. The crest on their face has yellow spikes curved upwards, red spikes on either side, and two grey spikes framing the mouth.

Entei

Volcano Pokémon

Height: 6ft 11in
Weight: 436.5lbs

This brawny Pokémon courses around the earth, spouting flames hotter than a volcano's magma

Suicune. Resembling a wolf, they have blue fur, with white diamond markings and a white belly. They have a flowing purple mane down their back, and their tail is twin white ribbons that flow forward. The large crest rising from their forehead is a blue hexagonal ring with small spikes at either side of the base.

Suicune

Aurora Pokémon

Height: 6ft 07in
Weight: 412.3lbs

This divine Pokémon blows around the world, always in search of a pure reservoir

The Crown City Beasts

Shiny Raikou, Entei, and Suicune appear in the movie Zoroark: Master of Illusions as the protectors of Crown City in Sinnoh.

Shiny Raikou, Entei, and Suicune. Their colors are different than usual, each feels more monochrome. Raikou's mane is yellow, Entei's red crest is black, and Suicune's mane is dark blue. Their other colors have shifted only slightly.

Other Appearances

The beasts feature in a few spin-off games, and of course Suicune stars in a movie (Entei does as well but he's not real. Will I talk about him anyway? I dunno yet.) I haven't played most of those games yet and it's been a bit since I've watched the anime. I will know and add more about these other beasties, someday. But honestly we're here cause I really like ↓that picture down there↓, not cause I have something to say.