Pirates! for the Amiga is one of the true classics.
The audio was top notch, especially in that era, and was often used in demonstrations to show how digital music is better than FM synthesis. The classical score that occurred during the game could even be played from a menu off of the main menu at any time.
The graphics were fairly good, although surpassed by many other games on the Amiga.
The game play was the most interesting aspect - unlike most games of that era (typically platformers and scrolling shoot'em ups), Pirates! featured opened ended play, where the player determined where to go, which country to fight for, and what to do. The entire map was accessible at all times, with no "progress" based limitations on where the player's fleet could be sailed. The player could be an all-out pirate, or fight for or against the English, French, Dutch, or Spanish. Gold could be earned by hauling goods between ports, by random piracy, or by hunting the Silver Train or Spanish Treasure Fleet. Play style combined aspects of RPG, asset management, fighting (as in Street Fighter, although simplified), naval navigation and combat simulation, which makes for a very broad, although not tremendously deep experience.
The Amiga version differs from the C64, Macintosh, and PC versions in that the sound and graphics were much better.
If you enjoyed this game, on any platform, it is highly recommended that you check out Sid Meyer's Pirates! for PC, Xbox, or PSP, as it has generally the same game play, but has updated 3D graphics and sound.