Well, of course, you can only have 65535 established connections sending data concurrently at a given point in time. But what I meant is, that is not the bottleneck at all, but the software behind handling all these requests, so tmartiro's comment was either pointless or sarcastic.

Note: This scenario is only valid for two computers talking to each other. As gilgoomesh said, if you have multiple clients you have virtually unlimited valid connection tuples (src addr, dst addr, src prt, dst prt).