My regular gaming group is an odd mix of software developers, lawyers, and theologians (okay maybe not that odd of a mix). We've been playing together, in various permutations of the group, for at least seven years (much longer for some). We've played games ranging from one-shots to truly Epic (both in mechanics and scope) 3e D&D games going to well above level 30. We rotate GMing responsibilities and experiment a lot in our games (only ones I run are accounted for in the link), usually around a d20 system fantasy base.
One area that we have spent a lot of time, and a lot of different games, messing with is the idea of levels and experience.
Experience points and levels are key features of D&D, its successors, and its derivatives. Through its long life and many iterations, the number of experience points (xp) needed to gain a level and the ways of obtaining them have varied considerably. In the earliest iterations of the game the majority of xp was gained through the acquisition of treasure (from which the core idea of treasure as a character reward and xp as a player reward is derived). In 2nd Edition AD&D, giving out individual xp rewards based on role-playing and player involvement was a core tenant. By 3rd Edition, the vast majority of experience was earned from combat. Likewise, experience to level ratio varied from 2500 for an early-edition wizard to reach 2nd level to only 300 for a character in the latest 5th edition.
With a large and slightly fluctuating gaming group with players with varied levels of real-world gaming experience (ranging in age from students in their 20s to professors in their 40s), varied preferences from stodgy table-top only gamers like myself to avid computer gamers, and varied preferred editions, how to award experience is often a point of contention. As a child of 2nd edition, I tend to run games that involve lots of situations which cannot be won by combat and, as a result, award the majority of experience for role-playing and story advancement. Another GM tends to run massive battles, with the expectation that the PCs will win, and thus gives out large amounts of combat-based xp. And some players have argued that we should try the truly old-school gold=xp. Then there is always the problem of players who missed a session due to real-life circumstances lagging behind the party (arguably through no fault of their own--we're all adults after all).
Our compromise: get rid of Experience Points all together.
In our last two games, one with a single-GM, another with collaborative rotating GMs, we did not issue experience points at all. Characters still gained levels, but these were entirely based on story events, and were applied to the party as a whole.
In the first such experiment, was an epic fantasy setting, where the party leveled whenever they achieved a major goal in overcoming the BBEG (destroying one of the artifacts from which he drew his power). This made the campaign very goal oriented--the party could bypass the optional treasure room, sneak around every fight, and still level, because they completed their mission.
In the second, a game based on imperial China, the party leveled by gaining increased titles and rank in the empire (vaguely similar to the idea of level-titles in OD&D). This has made for a very political campaign--the party gained levels by forging a document to give themselves a promotion (no combat, treasure, or even mission necessary), passing imperial exams, founding new temples, and winning military campaigns. The players have a lot of incentive to define their own role in the world and find their own path to getting promoted.
In both cases, everyone loved it. No more tedious tracking of xp (and going nuts when your character sheet gets lost), no more feeling left behind if you missed a major battle because your kid was sick, no more feeling railroaded into playing murder-hobos bent on getting every piece of treasure or solving every problem by force.
What can this tell us about levels and experience?
While levels are inherent to the system, experience is not. Levels represent milestones in the life of the character, points where they have achieved new knowledge and power. Experience is a way for the players to track incremental progress to towards that milestone, but otherwise serves no real purpose.
What if we got rid of levels altogether and only had story advancement?
The simple answer to this question would be: "Well then it just wouldn't be D&D anymore." A game with all first level characters can be fun, but at some point in the story even Samwise will become badass.
A slightly different answer would be to look at player expectations and that idea of milestones. Having played a lot of games, there comes a point where as a player I associate the GM saying "this game is going to be epic in scope" to mean "I have enough material that you should be over level 20 when the campaign ends". In our group's many collaborative campaign-building experiments, I have often heard the statement "where do we want this game to be when the players reach level 20?" If the Players Handbook has level charts that go to 10, or 20, or 30, there is an inherent expectation that the story you will be telling goes to that level as well.
Just as a story needs a beginning, middle, and end, or an author who is intending to write a trilogy thinks "what needs to happen in the middle of book 2 to make book 3 work", a GM writing a campaign can use milestones to help plan the story he intends to tell. Character levels become an easy gauge for that. When writing the campaign, I can easily think in terms of "the party should be level 5 when X happens".
By ditching experience points, but keeping levels, that mapping of story milestone to level becomes explicit and required. The GM can plan his story more efficiently, and, more importantly, the players get a real sense of achievement from leveling. Rather than thinking "oh look, I got 2000 xp, I level" it instead become "woohoo, we advanced the story by a stage". Levels are no longer a completely abstract award for having collecting however many thousand of this arbitrary currency of play we call experience, but instead are a direct reflection of the players' progress through the campaign.
A real milestone, a real reward, with a real sense of progress and accomplishment.