Pirate Junk is a web-based pirate sim with one major drawback — at the moment it only runs under IE.
If you can get past that, this is a typical trading sim set in the mid-19th century. The player starts off with a ship and a small inheritance. From there, the player can upgrade the ship, sign on crew, and purchase goods in one port to trade in other ports. The goal is to accumulate the most gold possible.
The game cites the 1980s classic Taipan as its inspiration, and it is a fairly deep game considering it is entirely browser-based.
You can sign up for a free trial, and unlimited play is just $5.99.