Not a fan.
Oh, I've had plenty of multi-class characters in my time. Most recently I played a gnome illusionist-assassin in a buddy's Labyrinth Lord game (using the Advanced Edition Companion, natch). Way back in my AD&D days, my longest running character was a 1st edition bard, about which I'm sure I've blogged at one time or another. When I played D20, I believe every single character I used was some sort of "multi-class" character...let's see, I had a wood elf ranger-barbarian, a human barbarian-fighter, a halfling monk-ninja, a dwarf fighter-rogue-duelist, and a half-elf ranger-bard-assassin. Most of these (including the dwarf and wood elf) were started at 1st level and "worked up;" others (the half-elf) were created as high level characters (using the DMG3 guidelines) to fit campaign specs.
[lot of fluff and nonsense for little gain. A lot of appeal to a a player's desire for customization and micro-managing, with the game itself suffering (all of these campaigns fell apart as the DMs got tired of tracking all the various PC capabilities while creating/juggling adequate/balanced challenges). Sometimes it got pretty ugly. These were not games with a lot of players. These were not DMs that had little experience, but individuals who'd been playing since the 80s]
I should also mention that I ran 3E games, and had similar breakdowns, not because I was incapable, but because the players kept screwing their shit up. I'd double-check their builds and point out errors and they'd throw up their hands and walk out.
[on a related note, I can see why D20 commands such devotion that people jumped to Pathfinder when WotC cancelled the line. If you put in the time and energy to make the system "hum," and you enjoy character customization, I'm not sure you could find a better game. At least not one that still uses class-level as a major system feature]
Whatever. I'm not a fan. For me, it doesn't make a whole helluva' lot o sense: it is damnably hard to work at two careers at a time, let alone three, especially ones with completely different skill sets. I can get behind elves being both magic-users and fighters due to their thousand year lifespan, their strangely fey brain, or their "inherently magical nature." For one particular species of demihuman: sure, it's okay. For everyone else? No. You learn one trade, and you become skilled in it, or you die.
I really don't want fighter-thieves or cleric-rangers or fighter-magic-user-thieves running around the game. It's messy, sure, but I just don't find it sensical. If a halfling can do it, why can't a human? Which appears to be the question the D20 developers asked themselves when designing the game. However, I would have come up with a different answer: you're right, they can't.
Oh, boo-hoo, I'm so anti-fun. First you spit on dragon born and tieflings and now you're taking away our ability to multi-task. JB, you Big Jerk, you. Yes, I'm a big jerk...one who's decided it's time to say:
"Enough fence-sitting. Pick a damn class."
If you don't like it, retire the character and pick a new class. This is one of the luxuries of playing a fantasy game: unlike real life, you're not really stuck with the choices you've made in life. Sure, I could go back to school to study international business or computer science or creative writing...but making that kind of life transition is pretty tough. And in my (fantasy) game world, it ain't an option. We're talking about an adventuring career, right? Professional football players take fewer hits, and they're retired by 30. Maybe some individuals will "dabble" in other classes -- picking up the ability to use a sword, or read a magic scroll -- but wholesale learning of multiple class features? Switching to a new set of class skills? No and no.
Elves are elves are elves, and their combo of magic and fighting gets to stay. Everyone else? Figure out what you want to be. 'Cause that's all you're going to get.