(or "Don't Stop Me If You've Heard This One")
Sometimes, people talk about how there are only thirty actual stories out there. Most of the differences we see are actually cosmetic, changes in setting or gender or name that don't really disguise the fact that this story is about Two Star-Crossed Lovers, or A Boy Who Becomes A Man. Depending on who you talk to, the number goes down even further (I've heard as few as seven.)
Certainly, the story of the Rawhide Kid feels like it's been written countless times. Even if you throw out all the changes in time and place and just look at other Westerns, it's still a pretty common yarn. It's the tale of a Boy on the Edge of Manhood, one who Learns How To Fight But Also When Not To Fight, from a Grizzled Old Mentor Who Is Slain Through Treachery. The Kid goes on to Avenge His Mentor's Death, but then is Mistaken For An Outlaw and Goes On The Lam, Doing Good Deeds While Outrunning The Law. And of course, he Never Starts A Fight, but he's Always Quick To Finish One because He Lives In A Lawless World Where Good Men Must Stand Up For The Helpless. (I'd include links to the appropriate pages on TVTropes.com, but I'd like you to someday finish reading this column.) Oh, and of course, His Reputation Means That Everyone Wants To Prove Themselves Against Him, one of the all-time classic Western tropes.
The storytelling engine is about as familiar as they come...but the reason it's familiar is because it's so tremendously useful that it gets used again and again. The Western setting is reused because it was a period filled with tremendous amounts of interesting and dramatic conflict; settlers fought natives, farmers fought ranchers, outlaws fought lawmen, miners fought claim-jumpers, humans fought nature, inventors fought the limits of human technology, and all with a sweep and scale that ranged over thousands of miles and several decades. There's enough interesting things happening during this time to support just about any number of potential sub-genres (as demonstrated by steampunk Westerns, zombie Westerns, alien Westerns, and in the case of Jonah Hex, all of the above at once.)
The Rawhide Kid becomes the character he is because of the usefulness of his storytelling engine. Characters that are too prone to violence become unsympathetic, while those that can't use it tend to have a hard time supporting a continuing series set in the Wild West. So the Kid becomes a reluctant, but amazingly talented gunfighter. Having him move around a lot means that you can involve him in all of the various Western sub-genres, not just a particular one, and having him be an outlaw simultaneously helps generate and sustain conflict (because anytime the law shows up, there's a chance he could be arrested, and so he can't always go to the sherriff when there's trouble) and also provides you with a rationale for his constant travels. (Which in turn provides you with another story-generating element, the Girl Who Falls In Love With The Kid But He Must Always Be Moving On. Mind you, over the course of this series the Kid moves on so many times with such speed and so little remorse, it's no wonder a later writer decided he was gay.)
Having a mentor provides you with a backstory, having him dead prevents you from having to worry about him dominating the story. (After all, if the hero is only beginning his journey, it follows his mentor would be more talented. It's never a good thing when the main character is outclassed by his supporting cast.) Every element of the Rawhide Kid's storytelling engine has had its rough edges and problems worn away by countless writers until it all fits together seamlessly. When you look at it like that, it's no wonder it crops up so often. After all, every change you would try to make to this to avoid the "same old story"...results in no story worth telling.