You wouldn't have high expectations for back story on a guy literally named "The Nameless One." Yet the customizable protagonist of Planescape: Torment has gone down as one of the all-time great heroes in video games.
Of course, the title of "hero" isn't always appropriate. The Nameless One begins Planescape as your average amnesiac. You built his stats like any other role-playing game character, and then made his choices for him in various ways. Which was appropriate, since the game was built around the world of Dungeons and Dragons.
Pretty quickly, however, players realized that he wasn't just any old cliché (though that wasn't a high bar for central characters in RPGs with memory loss). The Nameless One wasn't just a player-built character, but an immortal who basically set the stage for the entire, lengthy game ahead of you. Over thousands of years, he'd died, resurrected, lost his memories, rinsed, and repeated.
At least we hope he washed himself between incarnation. You see, the wrinkle with his immortality is that it isn't immortality at all. He can become corpse-ified like anyone else. The only difference is that he wakes up afterwards -- usually with no memory of his past lives.
This "reset" would cause him to become a completely different person each time The Nameless One "died." Various versions were kind, evil, insane, unpleasant, or just completely unnoticed. One particularly nasty incarnation valued practicality above all else, which made him one of the greatest villains of his era.
That was a big pair of shoes to fill, since The Nameless One's actions in his first life resulted in the entire multiverse being made to slowly die over the millennia. Granted, if we accidentally kick-started the heat death of everything, we'd want to forget about it, too. Yet The Nameless One we got in Planescape: Torment wasn't satisfied with just knowing that. Instead, the game teaches you eons of back story on his latest quest for redemption. Which transforms "The Nameless One" into a very notable character indeed.
In the very first Phoenix Wright: Ace Attorney, our titular star isn't much to write home about. He's got spiky hair, a memorable catch-phrase, and apparently only one suit in his wardrobe. That's about it.
If you were to jump from that game to the latest Ace Attorney game, you'd hardly recognize the guy. Well... You'd recognize him instantly. He still only has that one suit, after all. You would be completely lost when trying to untangle his murder-filled history, however. That's right. No matter how cheery, pun-filled, and colorful Phoenix's world becomes, we must never forget that it's built on the back of never-ending homicide.
We'll get back to that. For now, know that after three games of basically being an automatic pitching machine for platitudes about justice, Phoenix fucks up. He presents forged evidence (without knowing it, of course), and is forced to give up the one thing that defines him in his world of one-dimensional character traits.
In that time, Phoenix becomes a professional piano player, gambler, and a dad, after he adopts an orphan whose father was, of course, murdered. He also adopted a beanie and five o'clock shadow during this time, which everyone promptly forgot about.
The down-time was good for him, however. With the spotlight finally off of Phoenix, new playable characters were allowed to take center stage. Namely, Apollo Justice and Athena Cykes. This duo has been playable, alongside Phoenix, ever since. They also become his protégés, further distancing Phoenix from the role of a young, up-and-coming lawyer.
Instead, Phoenix Wright has oddly become a kind of authority figure. Besides taking care of teenagers, and solving crimes, he opens up his own legal firm -- the Wright Anything Agency. While it's couched in the same kind of pun that permeates Ace Attorney writing, it's a perfect sign of how much the character has grown from game, to game, to... game.
Whereas most video game characters tend to be ageless, and unchanging, Phoenix has done a lot of growing up since the Game Boy Advance days.