Honestly, it's all about balance. Games like Dungeons and Dragons are generally built from the ground up to support multiclassing. Each class has its synergies, and multiclassing its own rules, and there's a limited frame in which they work which works with the whole concept of multiclassing. With WoW, you have 10 separate classes so minutely balanced that even the slightest outside influence can shift the balance of power in class representation and role. With millions of players, each of them expecting to be able to fulfill a certain role and be competitive with everyone else, and each class balanced around a very specific set of skills and equipment, adding multiclassing to WoW would require such an extensive redesign that it would make Patch 4.0 look like a hot fix.
Of course, with that said, it's definitely fun to speculate on how multiclassed characters would work. After all, there's probably been a time for most of us when we've said, "If only I had that other class' ability." For me, I admit to want to play a nice affliction warlock/unholy death knight combo. I figure that with all the DoTs both classes can bring, plus Ebon Plaguebringer, I'd be pretty powerful. Then, maybe we cheat a little and let Pestilence spread Affliction lock DoTs too. I'd pretty much be an unstoppable god of annihilation and a textbook example of why there's no multiclassing in WoW.
So if you could grab a few skills from another class for your own new multiclass character, what would they be, and how would you use them?