privateers are one of those strange units. Most people build one send them after a galley, it gets sunk, and they never build another. The other annoying thing is if you leave one fortified outside one of your cities eventually an enemy vessel will come out of nowhere and sink it. It takes planning, commitment and strategy to use them effectivelly
One privateer is totally useless for combat, a stack of 5 or ten is a different animal. 5 privateers should be able to take out an ironclad. Use them in conjunction, with a few well positioned frigates and you have something useful.
They also can be used to gather intell, you can identify those cities that are defended by spearman instead of something more formidable.
I like to find AI vessels that are obviously sent out to colonize. Shadow them during the long voyage, and sink them just prior to landfall. I then will colonize the same square, as you know the AI often colonizes quite close to where a resource will appear in the future.