I don't multiclass, and in campaigns I run multiclassing is the only optional rule I absolutely refuse. I'll consider any other option, DMG or homebrew, my players are interested in, but not multiclassing, at least not at the beginning of a campaign.
That said, if a player came to me with a role-playing reason for his character to switch classes, I would consider that. I would first check to see whether the RP could be served with a feat, or even re-creating the character with a different archetype, but I would consider multiclassing in that situation as a last resort if there weren't another way to implement the character's narrative.
I don't have a problem with min/maxing within a class, but when min/max shenanigans include multiclassing you wind up with a crappy result. The whole "dip into class x" to pick up an ability annoys me a great deal, and it seems like the people who do that kind of crap never bother to consider how it makes any sense for a city rogue to suddenly become a barbarian for a couple of levels. D&D is escapist fantasy for me, the modern equivalent of sitting around the fire in the cave telling stories that help us to forget that there are sabre-toothed cats in the darkness who think we smell delicious. When you force me out of the narrative to focus entirely on class mechanics, I remember the predators (because frankly, that crap feels a lot like preparing my income tax return every year.)
So, I chose "I generally don't multiclass," because "Oh, hell no" wasn't on the list.