DS started playing independently around the time he started main school. Don't know exactly why but I suspect it was due to the independence given to him there, he was expected to do a bit of solo work, hand his coat up himself etc. Where as at nursery and at home with me it was either one on one or a very led environment IYSWIM?
He is still an only child, sometimes we play together and sometimes he does his own thing.
DS is 3.9 and is perfectly happy to play independently if I'm busy (e.g. cooking, cleaning, getting dressed). However, if he decides that I'm available (e.g. reading) then he insists that I play with him. Mostly I'm happy to play, but sometimes I negotiate 10 mins for a cup of tea - this works best if I tell him how long it will be until I'm playing again.
I have an only who is now 10. I operate much like Bandrchang. I realised that having an only I would have to make myself more available than I might be if I had more than 1, but if I have things to do I tell her I can play in half an hour for example.
My DD is 7 and hates playing by herself. She will play on her own for short periods, but will always ask us to come and play with her. I don't always understand her, as both DH and I grew up alone and were perfectly able and happy to entertain ourselves. She is a very social child, always looking for a friend and in the absence of friends she's looking to DH and me for companionship. I guess it depends on the specific child's personality!