I found If a Pirate I Must Be by Richard Sanders to be a very enjoyable read. It's about the Welsh pirate Bartholomew Roberts (the original "Dread Pirate Roberts", I guess, if you are a Princess Bride fan). Told me a lot of stuff about pirates that I never knew from movies and books like Treasure Island (which I would also suggest everyone read, because it's fantastic).
Of course, I entirely agree and it almost goes without saying that you should read A General History of The Robberies and Murders of the Most Notorious Pyrates by Captain Charles Johnson. I've also seen it published as A General History of the Pyrates and The Lives of the Most Notorious Pirates (I have copies of several different editions!). The original work from which we get most of our knowledge of the lives of the famous pirates, and which shaped our notions of what pirates were. I'd try and get an edition with the 18th Century illustrations in it, as they are pretty cool.