|Entei: derived from Inti, an Incan sun God||Entei: From the Japanese name "Entei"|
Game Boy games: Gold/Silver/Crystal
And you thought trying to get Moltres back in R/B/Y was hard. They really kicked it up in G/S/C trying to get the new legends. None of this "go to it"--nope, you have to let him come to you. Instead of just waiting patiently in one place, these bad boys (er...girls...er, whatever, I think he's male) run all up and down the damn map. Entei's location is almost random, but there's a way to find him. What you should do first is buy a bunch of max Repel and get Kurt to make you tons of Speed Balls, Friend Balls, and Heavy Balls. Fast Balls aren't too good.
Next, run around like an idiot until you see him. He'll take off the second you see him unless you use the Master Ball on him (and you only get one unless you shark, you punk). Then look on the Area command under Pokédex and you'll see where he is. He'll always be in the Johto area. DON'T FLY TO HIM. He'll run to the other side and it'll be lost. Go to a city, and then see if he's at least two areas away. If not, fly right back to where you are and shuffle it up again. The second he's close, douse yourself in Max Repel and wander into the grass with a Pokémon under level 40. This means the only Pokémon that you'll see will be a legend--most likely him. Try Sweet Scent as well.
The second you see him, make him sleep! Mean Look doesn't help, he'll roar and you'll run and you'll have to do it again. Hope you get first hits, and make sure that your Pokémon's faster than Entei. Once he's sleep, start to neatly whittle his health. This is where False Swipe is good, since it knocks him to 1 HP but will never kill. If you kill him, reset! There's only one in the game. If he runs before you get him, that's okay--he doesn't heal before the next encounter.
Once you got him, SAVE! You don't want to do this shit again! And like Moltres, there is no breeding, so you can't just spit out tons of Entei babies. He gets all the good Fire Moves--Flame Thrower, Fire Blast, and Fire Spin. I'd get rid of Roar, myself. But that's because I loathe the move.
Game Boy Advance: Ruby/Sapphire/Colosseum/FireRed/LeafGreen
Oh, honestly. You've got Latios and Latias to chase down. Do you really need a beast too? Do you? No. So he's not in Ruby/Sapphire.
He is in Colosseum, yes, but as a Shadow Pokémon. The first time you go to Mt. Battle you fight through nine normal people and the tenth guy is the boss, Shadow Leader Dakeem. He won't start out with Entei but Entei will come out after you kill one or two of his Pokémon based on how the randomizer goes. What you need to do is weaken him and then steal him from his trainer. Then you purify and viola!
In FireRed/LeafGreen Entei is the Beast that you get to chase down if you start with Bulbasaur in FireRed/LeafGreen. I won't be seeing one till I beat Colosseum, since I started with Charmander and so I get pretty Suicune. His Ability is Pressure: this means that for every move used against an enemy, the opponent uses twice the PP. It's a nice way of saying your opponent wets himself at the sight of Entei.
Entei is a badass Legendary Beast. Though personally, I love Suicune more. He does quite resemble a lion, which is why I look at the Beasts as cats, not dogs. He's definitely male, though. Just like Suicune is Female. (Don't look at me like that. My legends have genders.)