As characters meet monsters in mortal combat and defeat them, and when they obtain various forms of treasure (money, gems, jewelry, magical items, etc.), they gain "experience". This adds to their experience point total, gradually moving them upwards through the levels.–Dungeons & Dragons, Volume 1, p. 18 (1974)
The importance of finding treasure to a character's level advancement is a foundational feature of the Gygaxian presentation of D&D. In fact, after the publication of Greyhawk in 1975, which introduced a new – and less rewarding – method for calculating the XP of defeating monsters, finding treasure only rose became more importance. In AD&D, which uses a roughly similar system, Gygax explains that the system is intended to be an abstraction rather than reflective the in-game activities by which a character might "actually" advance in the skills and abilities of his chosen class.
I have never had any significant problems with this set-up. I accepted it without question when I was first introduced to D&D more than forty years ago and have made good use of it in multiple campaigns in the years since (including in my D&D-derived Empire of the Petal Throne campaign). I largely agree with Gygax that it's a perfectly workable compromise for a game whose rules don't (generally) possess a high degree of detail (see the one-minute combat round as another example of this in action).
However – you knew there'd be a "however" – I've been thinking lately about the need for experience and advancement systems for roleplaying games. In doing so, I began to think about the idea of using gold and other monetary treasure in a slightly different way. In Chaosium's RuneQuest, characters can improve both characteristics and skills through training. This training takes two things: time and money. A character who lacks either cannot make use of this method of improvement and must instead rely on the much more unpredictable method of experience rolls after the successful use of a skill in an adventure. It's worth noting, too, that even spells are acquired by "buying" them, usually from a cult.
Beginning characters often lack sufficient funds to buy all the training and spells they desire. That's why the cults and guilds of RuneQuest sometimes extend credit to neophytes, enabling them to take on a debt in exchange for training. This not only makes beginning characters a little more prepared for the adventuring life than they would otherwise be, but it establishes a connection between the character and the cult. In this way, beginning characters are immediately connected to the setting, one the referee can then use in the course of the campaign. It's an inspired idea to my mind and one I think more games should look to for inspiration.
This brings me back to the use of gold as a measure of experience in Dungeons & Dragons. As I've been thinking about this matter, I find myself wanting something akin to RuneQuest. Instead of a character simply improving all of his class-based abilities as soon as his experience total reaches a certain threshold, wouldn't it be more interesting – I won't say "realistic" – if instead he could use his gold to buy training that improved his abilities piecemeal. For example, he could employ a weapons master to increase his combat skills or acquire access to new spells at the sorcerer's guild and so on. Even mechanics like hit points and saving throws could be acquired through training of some sort or another.
Now, I realize that AD&D at least already possesses training rules and that, to some extent, they exist to explain the purpose of the large sums of money needed to gain new levels. However, like so much in D&D and its descendants, they're very abstract, more abstract, I would argue, than many similar systems in the game. Mind you, I speak from some degree of ignorance, since I cannot recall ever having made use of these rules, nor did I ever know anyone who had, until relatively recently. It's quite possible that AD&D's rules work very well and achieve the kind of in-setting connection I increasingly see as vital to a campaign's long term success.
One thing the AD&D training rules do seem to do is take time. Much like those in RuneQuest, a character will spend weeks of in-game time training the new abilities he's acquired upon gaining a level. That's something I very much appreciate. Between my House of Worms campaign and the Pendragon campaign in which I'm currently playing, I am more convinced than ever that a long campaign should encompass years or in-game time, with characters and events growing and changing in the process. This is an area where RPGs excel and it ought to be embraced.