There's some discussion out there in the OSR blogosphere about demihuman level limits. Some people, as has always been the case, hate them and refuse to use them. Others think that they are a necessary part of the game, and useful to emphasize the humanocentric nature of the sort of swords & sorcery fantasy that is the implied subject of most games with levels. Certainly, the increased numbers of players with demihuman characters in modern D&D games would seem to indicate that there should be some sort of factor to discourage their play. The question is, should that factor be something so seemingly metagame-y as level limits.
It's important, I think, to figure out just what character levels and experience points represent in the game. That is, what are they, besides a game convenience? The normal idea is that levels represent a level of skill and training. This is supported by the idea of training for level increases in the 1E DMG. However, it is countered by looking at what events garner experience points, and by examining some other issues. For instance, a 1st-level Fighting Man is not described as being in training: he is called a "Veteran" in the editions which used level titles. That is, he is someone who has already learned the techniques of his craft and had occasion to apply them in practice. He is a veteran, not a tyro. Similarly, as Talysman points out, the Magic User and the Cleric imply that the starting character has learned what he can from his instructors. And experience points are not given for training, or even for practicing skills. They are given for acquiring treasure and destroying (or defeating, in some formulations) foes.
So, why would a character have experience points in exchange for picking up some coins or for putting a sword through the heart of a goblin? I think that the answer is to be found in another game, Pendragon. In that game, an analogous quantity called Glory is the goal of the players. Glory is acquired for similar (though not identical) reasons as experience points. The amount of Glory gained represents the reputation, temporal power, and spiritual accomplishment of the character. Similarly, experience points (and therefore levels) seem to represent the success and worldly power of the character. That is, it is a concept very similar to the Polynesian, specifically Maori, concept of mana (not to be confused with the appropriation of that term in gaming to mean, merely, "magic points"; as an aside, I'm curious to know where the earliest use of the term in that capacity occurred). That is, it is authority and luck and reputation and power and confidence (both self- and that of others).
Now, given that, it becomes more obvious as to why demihumans, in a humanocentric, sword & sorcery world, have level limits. As Talysman notes, elves and dwarves and halflings are all seen as secondary to human concerns. Not many humans, in such worlds, will subject themselves to even elven kings, much less dwarven or (ha!) hobbit ones. Humans are the measure of all things in such worlds, and it is only they who can reach the highest realms of authority and power, not only in the realm of temporal power and politics, but in the more mystic worlds of arcane and clerical magic. This is further borne out by the later Thief class, which did not limit levels of demihumans, but which is the most mundane class of them all, with little interest in the rarefied realms of political, arcane, or spiritual power.
So, level limits seem important for both metagame reasons (discouraging the use of demihuman characters without artificial "balancing") and for reasons of simulation within the context of the material. It's only those games which didn't share that context that made the limits nonsensical (but, then, there are many other aspects of the rules which wouldn't then fit into those games). This is interesting to consider in context of the WRG Ancients RPG I am working on.