Sid Meiers Pirates! has a few important features that define it as well as any single genre will:
- role-playing elements
- NPC alignment
Some games that fit a number of those features are Oblivion, Fable, and Eve Online.
Oblivion and Fable are both rpgs that are vastly open-world, with alignment systems where certain groups of NPCs are for or against you depending on your actions (compare with your allegiance chosen in Pirates), and some elements of commerce where you may own stores, trade, and partially influence in-game economies (similar to trading in-town in Pirates).
Eve Online fits more features than Oblivion and Fable, as it is an MMORPG with battles similar to those seen in Pirates and fleshed out commerce with player-owned corporations and player-controlled merchants.
Hope this helps direct your search.