We use real plates and real silverware. If it's just our immediate family we'll use the "fine china" (though ours is actually some keepsake cobalt blue glass), if it's the extended family we'll use the everyday plates and silverware.
Food/dinnertime is ... kind of sacred in my family... serving people on paper plates or with disposable silverware would be considered by my dad to be "not loving the family." We all pitch in to wash the dishes that won't fit or are too delicate for the dishwasher, so there's really no reason to go disposable.
I'm nowhere near as particular if I'm eating at someone else's home, a paper plate (doubled up so it doesn't flop) doesn't really hurt the quality of food at all. I do actually carry a metal fork, spoon, and knife in my backpack, though, because food just doesn't taste the same off of plastic cutlery---for when I'm eating by myself. But if someone serves plastic cutlery, I'll suck it up and use it. No sense hurting anyone's feelings.
But yeah, in the home I grew up in---disposable dinnerware is kind of forbidden. I think we do have a small stack of paper plates in the bottom of some cabinet so mom can give food to guests who are about to leave without losing one of her plates forever, but that's the only purpose they serve.