Growing up, on my mother's side of the family, us kids were sent off to play, the menfolk helped clear the table, then set up for after dinner activities (card playing or what not), and the women did the dishes. Things went pretty quickly as I come from a large family.
We didn't do big family dinners on my dad's side, but I do know that when we went to visit, the grandkids did the dishes.
At home, my sister and I did the dishes every single night for at least 8 years, having the "I'm rinsing" argument at least three times a week.
My husband and I share the kitchen chores and are teaching the kids to do them as well. I make dinner most nights, but on nights I can't do it (ie new baby, morning sickness, afternoon activity) he has no problems with making dinner, and rather likes to. (He taught me to cook, he's good at it.
) When we have company, I don't want them in the kitchen, I want them to relax. DH and I make most things ahead of time and just have dishes to wash after they leave.
Dinners at my parent's house are so seldom now, and usually in the summer when we visit, so it's burgers on the grill with paper plates, very little clean up.
Dinner with the IL's I have no idea who does the cleaning. I don't, because I can't make heads or tails of my mil's kitchen, it's pretty cluttered, so I don't even try. (Then again, I try very hard to eat there, for that very reason.)