I find it bizarre that the pirates keep on popping up out of nothingness. This really ticks me off. I have seen some suggestions on the forums about having pirate bases and the like.
I think that this is a move in the right direction. However, it is too simple. If pirates were spawned from a few obvious pirate bases, then it would be (relatively) easy to take them out, and not have to worry/be annoyed by them for the rest of the game.
Therefore, it is my opinion that if the pirates have their own bases and such, the bases should be very, VERY difficult to find in the first place. The hypothetical bases should reside in asteroid fields that are unseen on the field. Their phase lines do not show up, therefore no one knows that they are there. Imagine this:
You have been raided by pirates periodically throughout the game, and enough is enough. Equipped with an Arcova scout frigate, and having researched a new ability that is far, far up the research tree, you travel to a system where the pirates frequently appear. Once there, you set off the scout's new ability, an advanced sensor array thingy. And what do you know! A new phase line appears, leading off to a previously un-discovered asteroid field, which is swarming with pirates!
Once the pirates are wiped out, you could then colonize the hidden asteroid field, giving you a secret base from which you could launch surprise attacks upon your enemies.
While taking care of the spontaneously materializing pirate problem, it would also add an element of suspense and intrigue to the game.