Although I believe multiclassing has its place, I feel that the modern, "take a class level here, take a class level there" style represents neither the kinds of fiction I like to model, nor reality, very closely. This is chiefly because I feel the first level of experience represents a long background of training and study, but also because being good at one thing doesn't necessarily prepare you to be good at another, especially something that isn't closely related. And here, by "good", I mean "has a level's worth of experience".
As a case in point, Michael Jordan's Baseball career. No doubt he was a better baseball player than I am, but a .202 batting record in the minors and an undistinguished performance as an outfielder does not speak well to the idea that he "took a level" in baseball. Less so if we consider that some of that performance was due to raw athletic talent (a high DEX and CON, say, in D&D terms).
In the pulp source materials for D&D, some exceptions are bound to occur. The Grey Mouser, for instance: is he a M-U/Thief? Perhaps, although his actual spellcasting in the stories is limited, and not too far out of line with thieves' skills anyhow. And Elric? Isn't he a Fighter/M-U/Cleric? Doubtful. He isn't much of a fighter at all without Stormbringer, and he hardly "worships" Arioch (or any other god). He's pretty much a straight-up M-U with some specialty magic items that allow him to function on the battlefield, but that don't make him a "Fighter" in the D&D sense at all.
That's why I feel that multiclassing should be used as a personalization of last resort when deciding what your character can and can't do. In OD&D, what you could do, regardless of class, was far wider than it is today, or even than it was in 1st edition AD&D. You want your M-U to sneak around, lob oil flasks at monsters, and devise some contraption to break down a heavy door? Describe how to do it, and (within reason) it shall be done. I like it that way.