If you liked Privateer, Independence War 2 is in a similar vein. The "Torn Stars" mod for it really opens it up, too. Freelancer is also a good alternative.
Probably worth pointing out that Vega Strike is a Privateer-ish game--in fact, I think they implemented the Privateer campaign in it. It's very much meant to be an homage to that game. I, personally, have just found it kinda slow and buggy, but that could be my computer's fault.