urbancamper
Chieftain
Barbs certainly pillage, often annoyingly aggressively. They seem to tend to prefer to pillage things that are in a city's third ring; there may be some AI "avoid idling in the same square if you can be city bombarded from that square" thing going on, or it could be an illusion, but they'll usually crush things in your third ring, particularly special resources. They pillage farms/mines/posts much less often in my experience, and I don't think I've ever seen one pillage a road or a fishing boats.
I had a barb pillage a section of the Silk Road that caused the whole west side of my empire (Persia/India/Arabia) to disconnect from my Capital while playing through the Mongol scenario on Deity. I was like OMFG, barb, you're screwing up my delicately balanced happiness and economy worse than every other AI unit combined.