Thought I would add my own experience, in brief.
I am an only child, but my parents separated when I was young so I spent most of my formative years in a house with just my mum and myself. The dynamic is different I think to when an only child lives with both parents, because you can become so interdependent. My mum worked long hours and did regular business travel, so I was angry and frustrated by being left alone as there was no one else for me to be with at home when she wasn't there. On the flip side, after the rebelling (largely early on, due to the loneliness) my mum and I became very close and very good friends. Undoubtedly it was easier for her to 'spoil' me as it was just us, so we would go the cinema and out for meals regularly, we got takeaways, rented movies, went shopping, went travelling... it was easy to do as she only had the one child and I just continued to grow, there was no starting again with another.
Once I got into the tween/early teen years, I had a spell in which I wished I had a sibling. But, I wished I had an older sibling, as most of my friends did and I wanted that relationship of having an older brother or sister to look out for me - probably influenced in part due to the aforementioned time alone when my mum was busy. I never missed having someone else close in age to me and certainly wasn't after a younger sibling. I also come from a very small extended family, and we don't even see each other that often (once a year at best, save for my parents).
DH otoh has 3 much younger siblings and a large extended family. What seems to have had the most important impact is how their family works and interacts, not the number. DH's family, whilst large, is riddled with inter-family disputes, backbiting, and gossiping, and he generally dislikes being around most of them. He cares for his siblings a great deal and keeps in touch with them, as due to the age gap he has always acted 'fatherly' with them. But he left home long before they'd made their way through their teen years so he didn't grow up with them as such. My comparatively tiny family, whilst not very close, is very friendly, no arguments, no negativity.
As for cousins etc, that's unlikely to happen for quite some time for our DC. The only siblings are DH's, and they're all quite young so it will be some years before any of them even contemplate children. In terms of interaction and playmates it all comes down to our friends with children, and that works quite fine for me as they're people I know and get on very well with already, rather than people I hang out with because they have children.