I suggest anything by Alestorm, they're a pirate metal band (and my favourite band at that!). Pirate Song, Black Sails at Midnight, Captain Morgan's Revenge and Shipwrecked are especially good :)
One Hundred Bottles Of Beer!!!
Row, Row Your Boat!
Here is a drinking song, the cowboys sang it but the pirates should have too... You might recall Tex Ritter, the 1940's and '50's? I just learned John Ritter is his son!
"Whiskey Rye Whiskey...if a tree don't fall on me, I'll live till I die..."