Pokemon-like Rivalries

[JakeNubbin]

I've played my share of Pokemon games (three) and I've absolutely loved the rivals in those games. Everything else is just standard to me except for the rival system. Gary MF Oak or some other asshole challenges me to a fight and i get to see how well they've trained and matured and gotten stronger (not to mention that those are the only fights in Pokemon that you can actually loose without the ability to go back to a Joy center). What I'm trying to get at is if there are any other games with a similar system? I'm not talking about sequel transcending,like a boss returning in the sequel (as a robot). I also want to steer clear of just, repeated bosses, like fighting a juggernaut boss multiple times. You get to know this person and he/she returns over and over again like Riku from Kingdom Hearts (kind of). Or maybe Virgil from Devil May Cry 3 but you only fight him twice. I'd appreciate the help because I would love to see this element in more games.

 

[Trippy Turtle]

I don't know many games like that but if you want to try another pokemon game then I would suggest Pokemon Genesis.
Its a mod for pokemon fire red that completely redoes the game and makes new story, region and has about 400 pokemon in it.
Also I'm assuming you have Fire red.

 

[StorytellingIsAMust]

Each Phoenix Wright game has a recurring rival prosecutor or inspector that you match wits against over the course of the game. The relationship between the two is usually very interesting, as both Phoenix and his rival want to catch the culprit behind each crime, but their occupations put them against one another right from the start. There's really good character growth for them all throughout.

Legend of Zelda: Skyward Sword has a sort of rival-type boss, although you're really just fighting the main villain multiple times throughout the story.

Castlevania: Circle of Moon has recurring battles with a rival vampire hunter who actually was raised by the same guy as you and is pretty much your brother, but just became a real asshole by the time Dracula shows up. That's pretty fun.