I don't mind reusing characters that were in short-lived games. Occasionally, I'll 'reuse' a character in an RPG that's actually from one of my fanfics or original stories; this is because I want to push the limits on that character and see how far to go while staying basically the same person.
I do pretty much the exact same thing. In fact, most of my characters are re-used several times. I have a "character bank" consisting of twenty or so characters that I'm planning on using in original stories (some of which I don't even have sign-ups for yet). And the main way I develop and get to know them better is by participating in RPG's with them. So I encourage everyone who is an avid writer, particularly of novels, to re-use characters. It really helps you develop them, and can give you ideas for your own stories. Or at least that's what's been happening with me.
On another note, I posted a
Character Recycling Guide in the "Making a Sign-Up" thread in the main RPG forum. While I do believe in re-using characters, I believe that one must be smart about doing so. I've seen a few people copy-and-paste signups, and this really annoys me because they clearly have no concern for the RPG they're signing up for. Whenever I re-use a character, I mold them to the situation, which often causes me to modify or re-write parts of the signup. I can get away with copy-and-pasting some things (like Personality), but not everything.
As far as using characters on different platforms goes... I say it can be done. So far I can think of an example where I used the same character for a Pokemon RPG, an X-Men RPG, and a Persona RPG. Her personality was pretty much the same in all three; I just had to make minor modifications to her Appearance (not to mention I had to add superhero clothes in the X-Men RPG, and then I had to give her either Pokemon, powers, or a Persona depending on the RPG, which wasn't too hard. Changing the History just involved modifying her hometown and re-writing the last few paragraphs in accordance with the plot.
Also, I know of one user here (DVB) who uses the exact same character for every RPG he signs up in, no matter what the setting. Yet somehow, everything works out. He modifies things like Appearance and History in accordance with the RPG, and sometimes even makes him a different species or something. I can't tell you how many faces of Diego Vendrix I've seen: an ice ninja, a high school kid, a musician, a Pokemon trainer, and even a werewolf! But every RPer has their own style, and everyone just has to figure out how to make that style work. DVB certainly did.