I cannot answer your question on how many aircraft are actually airborne over the world at any one time. However, a lot of people assume that the big airline have more aeroplanes than they do actually have. The reason for this is that the airlines 'turn around' aircraft very quickly. The reason? If they're on the ground, they're not making money. So at any given domestic airport you might be seeing the same aircraft come and go several times in one day.
I spent eleven years in Civil Aviation as an Aero-ground operator (bit like an air-traffic controller) so you can take my word for it. There seems to be far more planes than there actually are.