I am one of double figures.
We all have very small families ourselves. The largest number is 3, and in each of those families, I know that at least one of the children was unplanned. I think this is very telling.
Pros
You learn how to get along or at least stay out of sight
You become very independant
Parenthood is not a shock to the system because you've been caring for babies since you were small
You learn that money isn't the cure for anything and how to get along on very little.
Cons
Where to start? With the best will in the world, my parents and the parents of all the large families I know simply can't give very much individual attention to anyone. Essentially I brought myself up and was responsible for parenting my younger siblings.
Children can hunt in packs. They gang up on each other and are ruthless with the weak.
The constant noise, the constant fighting, the crowd, the bickering etc can impact greatly on your sense of self.
You are never the best at anything, there's always someone else who can outshine you.
People outside the family can forget your name. Don't laugh, I spent much of my school years being addressed by my elder sister's name because by the time I hit the school, so many of us had gone through that the teachers gave up trying to distinguish us from each other.
You are never an individual. To take the education example again, my elder sisters are very good artists. It was assumed that as a girl of the same family I would be too. Every year I had the experience of being called to the front of the class, being handed a piece of chalk and being expected to draw something because "we were all so talented". I can't draw a straight line without a ruler but I'm a whiz at maths. Unfortunately my siblings aren't so I was always automatically put in the lower groups.
I don't want to put a downer on any Walton's Family hopes and dreams, but I found the experience of growing up in a large family horrific. I get on with (most) of my siblings, but I live half the world away and speak to them, at best, once a year. We are all a bit like that. It's not something I would willingly inflict on anyone I loved.