I remember when multi-classed characters appealed to me. I was a beginning role-player, and in Basic/Expert D&D there was only one multi-class option: the elf. Who wouldn't want to wield magic and weaponry and wear armor? One of the greatest attractions of AD&D for me and, I suspect, many others, was the dizzying array of multi-class options. In some ways they made little sense with their arbitrary limits, but the fact that there were so many choices was a strong lure for many gamers. The side effect (at least in my group) was that the ratio of demi-human player characters to human player characters was much higher than their populations in the campaign world. For some players, the preference was based on special capabilities, such as multi-class; for others it was the desire to play an exotic character; for many it was both. I wonder, though, how popular the demi-humans would be if they were functionally identical to humans and differed only in their culture, history, and physical appearance. Perhaps that would be an interesting alternative to explore.
Multi-class options largely bore me now because they water down the classes. Classes are a feature of D&D. If one doesn't like it, one should play a skill-based role-playing game (which is actually my preferred kind). As long as you are using classes at all, you might as well play to their strengths. A character with a class (as opposed to a 0 level character) has a special status in society as well as special capabilities. Let that class inform the development of your character. Instead of the irrational limits of D&D and the multi-class free-for-all of the Labyrinth Lord Advanced Edition Companion (forgive the hyperbole), try eliminating all multi-class options and level limits, but allow demi-humans to choose any one class just as humans do. Dwarves, elves, and halflings can be clerics, fighters, magic-users, and thieves. They have no limit to their potential advancement, but they can only choose one class. What makes demi-humans special is the way they are role-played. Allow them their minor abilities, such as the elf's heightened ability to detect secret doors, but don't allow them to be experts at everything (or nearly everything). It just might encourage more players to play humans and reserve the playing of demi-humans to those players most interested in playing them for their own sake rather than for the multi-class advantage. That, I think, is where I am headed.
[See also For the Multi-Classed.]