7th Sea is another one where you get XP when your background is resolved, and you then pick another (e.g New rival, new lost lover, etc).
7th Sea was exactly the system I was going to mention when I saw the topic.
What's interesting about how 7th Sea does it is that every character at the start of the campaign can buy 3 points of backgrounds in any combination (three 1-pointers, a 1-pointer and a 2-pointer, a single 3 pointer) and the bigger the number, the more frequency, importance and difficulty that background will have on the character during play. A 1-point 'Rivalry' might be with an old school chum that you rarely see anymore. a 3-point 'Rivalry' might be with another member of The Musketeers (of which you are a member). Any time the background "comes up" in some form or fashion during a game session, you'll get an extra XP point equal to the level of the background. Then eventually when the background is "resolved" (IE the problem is fixed), you earn three times the level of the background for that session. Then, at any point after that you can purchase a new background that you find yourself in if you have the points available.
So if you were to resolve your 3-point 'Rivalry' background (you quit the Musketeers because your rival became the head of the group and you quit in a huff)... you then had 3 background points to now spend on other ones that might have come up over play. Perhaps you spend 2 points on the 'Hunted' background because you took one of the Musketeer's puzzle swords with you when you left and they are going to continually try and retrieve it, and then you save the 1-point remaining for some other background that might come up later.
And to top it off... for any player that really wanted to go crazy, there was an Advantage you could buy at character creation called 'Foul Weather Jack', which gave you a single
4-point background (the only one you were allowed to have) that basically was one of the most dominant features of your character because at 4 points it assured that the background involved one of the most important people or most difficult situations in all of Theah. So like your Foul Weather Jack is 'Hated Relative' because you are the brother of the Emperor of Montaigne (the most powerful and richest person in all of Theah). And because the Emperor's reach and resources are so long... you pretty much have to deal with being his hated brother all the time.
It's a really interesting and cool concept for an RPG and it really draws players into the 7th Sea world (in the several campaigns I've been a part of.) The only kind of a pain is on the GMs part though, as he has to somehow work in one to three background per PC into various game sessions every week. The more PCs there are, that's more backgrounds that need attribution during game sessions, and things can occasionally get a little out of hand if the GM isn't really good at weaving threads together.