I've tried writing this several times and it hasn't gone well, so let me just get into the heart of the matter. Now, I know that a character is fully the property of its creator, at least among amateur-made things where contracts haven't been added to the mix, and when role playing it's extremely annoying for someone to try to change your character for you without asking. However, why does that bar people from even considering a change to or touch on their characters' backstories when it's done politely for the sake of story?
Now, I don't feel like a long argument about why this would make for stories that are better than a lot of the ones people do anyway. I could justify my reasons for thinking that if I really wanted to, and if you plan on attacking this entry based on their omission then try talking to me first. But with after all the stupid arguments and insults from people who don't think that I should even be allowed to write longer posts than they, shorter, more of less detailed stories, or plans for RP's before they start, I'd rather skip the likely fruitless endeavor. Instead, let me just point out that such stories would be DIFFERENT.
Now, if you're the type of gamer whose character will accept and fight for, and even confide in anyone supposedly on his side for no reason or even evidence of that, then making a character be your character's long-time friend will have little effect on their interaction. However, for people who don't do that - and I'm not saying it's wrong to do that; it leads to a certain kind of story that you may like - the effect will be clear. Even for people who do little in the way of character interaction, having it established that characters met in the past can lead to interesting events in the present. And for people like me, who often play antagonists, a character who clashes with another because of differing viewpoints but no personal reasons is a far different from one who does so because of or despite past relationships. One can also tailor-make a 'villain' to be something the 'hero' can't accept existing, an example that proves or at least suggests that everything about him and his beliefs are wrong. This comes very close to giving characters shared backstories, however, because it will involve taking a close look at one and making the other an eerie reflection of it, something the first player should notice eventually.
If anyone was reading this, some would probably be 'screaming' about how doing this would ruin their characters, making them different from what they wanted. Why is that? Your character had friends in school, right? Why is their fate so developed and important to who your character becomes that another character showing up and claiming to be one would change everything? It would change the present RP, yes, but in either case your character hasn't seen this person in the same amount of time - he wasn't there messing with him since high school or whatever. There are more ways than that, too. In a large number of these RP's, the characters are incredible, fantastic...abnormal, in any case. I can write a character into a super hero's backstory without changing anything. It's easy: How much collateral damage does a superhero fight cause? No one lost anything in that? Can a hero ever save every person? No - can someone blame him over the ones who were missed? Is it impossible for one of those people with the sort of tentative hold to sanity that makes them base their lives around a movie and think it's real instead see him flying overhead or fighting a bad guy and then act on it? All of these ideas suggest shared history, at least to the degree that the new character was present at some event in the other character's life and that time has passed since then for the new character to prepare. They would have no effect on the first character's past, and similar things can be found for any sort of RP.
To the people who are still uncomfortable with this thought, I ask why? They're just characters. If there's sentimental value in one I understand not changing, but most characters are just interesting ideas you had, right? Even if they were to be changed drastically, why would that cause a problem? Nothing says that you have to keep the changes for every RP, just the one they were made for. Why does it matter as long as it's to make the RP more fun and you actually discuss the best way to do it first? Think about comics for a moment. In comics and their movie/cartoon spinoffs, the same character is often redone several different ways with several different histories. However, each version is recognizable as the original character, and not just because he's wearing the same basic costume. Some key, formative points are kept basically the same in his history and have the same effect on the guy. You can do the same with your character that you roleplay with.
For the sake of anyone who was interested, I will now give an example. I think I'll stick with super heroes to make it easy.
Okay, as the story starts off, the first character, we'll call him Blue, is more of a super villain than a super hero. He isn't quite that bad, but he's using his new powers selfishly, taking revenge on people who wronged him. For the most part he's just scaring them and damaging their things, but then he messes up and one is hurt or killed. He is filled with guilt and, after a long, soul-searching experience he ends up working to help people and make up for it (I don't have time to figure it all out right now). The main RP would start sometime after that. Now, the second player could take his character from a number of points in this for what I'm talking about. The injured person could heal, if dead he could be bought back somehow. Family and friends of this person could show up, as well as witnesses. Which one, how it's developed, and what side they're on could all lead to very different games. This is a very basic example because I want to finish this up and post it. A more detailed story could yield a number of possibilities. Why not give it a try?