(Bah. I may have screwed up the scheduling of this one, so if it double posts or something, my apologies)
I've been chewing on games with more potent characters with the issues that that entails. One of the real issues is that once characters are at a certain level of effectiveness, advancement becomes a secondary. Characters are more about what they do than what they might be able to do someday.
Now, this is not a tirade against advancement. It's a fun part of games, and the classic D&D model of advancement makes for a fun minigame while the setting are designed to work with the logic of the level spread. The problem is that it's something that people expect from a game, and it's not always a good fit.
Some games absolutely support a model where characters get more powerful over time, sometimes drastically so. Level based advancement is the best example of this, but it can apply just as strongly to point based systems like GURPS or the nWoD. I consider this to be "vertical" advancement - the character's power goes up.
This is an idea that is probably better supported in gaming than it is in fiction. There are examples in the Luke Skywalker mode, but ironically those examples are often too fast for the taste of games since they tend to hinge on broad, universal insights or enough power to create temptation.
But the point to that all is that there are plenty of genres where drastic improvement seems inappropriate. Some might support a small amount of improvement over time, but compare, say, a western with D&D and the difference between a novice and an expert illustrates the point well. But people expect advancement, whether its appropriate or not, and that's a reality that it's worth paying attention to. They're not sheep or fools - they know what's fun and they have every reason to expect how to go about it.
So the challenge is how to come up with a system of "horizontal" advancement - one that can model characters growing and changing without them necessarily getting more powerful.
Spirit of the Century uses a model that allows for rearrangement within the existing framework. There's a little verticality in that you might gain a few more stunts, but your core list of skills and aspects doesn't get any longer. You can just swap things out within them. This made a lot of sense in intellectual terms: SOTC characters are already on top of their game, and since there's no guarantee that ever player will be at every session, the desire was to keep there form being any kind of power disparity. But this was not ultimately satisfying to players, and advancement is a popular tack-on. As much as this made sense for us, it's not a tack I would suggest anyone take.
For the Road to Amber MUSH, we added a currency to the game called "Focus" - it accrued much more quickly than XP, but it capped out at 10 points, so it was a "use it or lose it resource". In game, it represented time offscreen and how it was spent, so it could be use to do things like learn lores, make items, do research, pursue agendas and so on. It couldn't be used to improve skills directly, but learning lores or solving puzzled often opened opportunities to spend advancement on skills that would not normally be available.
It was a gigantic success, and by my understanding the idea has been adapted to a number of other MUSHes, with the details changed appropriately from game to game. My conclusion from this is startlingly banal: people love to spend points and by giving them more points to spend, they got more excited about spending them. It would not take much tweaking to adapt this to the tabletop, simply handing out points at downtime rather than counting on a timed distribution.
The trick, however, is what you can spend them on. Training is a good option, if your system supports that idea. Ritual magic and crafting absolutely. Research and Lores if your system has those, though few do in any kind of useful ways.
Personally, I like the idea of using these points for building and maintaining relationships. NPCs are a subject that can be handled more effectively on the tabletop than in a large scale game, and it would not be hard to marry some currency to a relationship map. This idea that relationships can be maintained or strengthened can also apply to things like resources and contacts. Certainly, there's a bit of a balancing act: you want there to be enough cost of maintenance to encourage re-investment, but not so much to just feel like a treadmill.
Now, there are other ways to approach this too, and I encourage thinking about the other ways you can provide your players rewards they can spend. The alternative is that you end up with painful treadmills, like the Amber DRPG advancement model (which was ultimately just a joke on the players)
1 - Point based systems have the advantage of allowing the game to have all the advancement "baked in" by simply starting the characters with a healthy dose of XP/points and then giving very little (or no) further advancement. WHile you can technically do this with a level based system, it tends to only work well for short games, since advancement is such an essential part of play in a level-baed game.
2 - WEGs Star Wars posited that the "Skywalker gene" allowed a character to advance in force skills for half the normal cost, which is why your jedi was never going to be as awesome as Luke. This was, to put it bluntly, kind of crappy.
3 - Drastic advancement tends to go hand in hand with fantastic elements. This is partly genre habit, but it's also because it is easier to model drastic, concrete differences between magics/psi/superpowers and so on than it is within the realm of normal human endeavor. Not that drastic differences don't exist in the mundane world, but learning enough to grasp them is a lot harder than learning to read a spell block.
4 - It may seem silly to couch it in those terms, but don't laugh it off entirely. There's a reason that white wolf keeps using dots to represent what are ultimately numeric values: it's just fun to fill in little circles. Never underestimate the awesome power of trivial joys.
5 - Curiously, this abstraction also addressed a lot of the problems of more structured "downtime" mechanics. If we had put in rules for training and research and other subsystems, people would have never touched them, but by giving them points to spend, they motivated _themselves_.
6 - Oh Weapons of the Gods, you beautiful, beautiful, intensely-painful to replicate thing.
7. But not as stupid as the Immaculate Conception of Darth Vader.