Pirates! may have possibly been the first open-world game I ever played. Long before I was running over pedestrians in GTA, I was raiding coastal fortresses and courting governor's daughters in Pirates! While Civilization will always get the bulk of attention when Sid Meier is mentioned, Pirates! actually predates it by a few years, and can arguably be considered one of the first open-world games.
I personally started playing the game with the Sega Genesis release, but there are older, more basic versions, as well as revamped newer versions for pretty much anything (sorry Linux users, I think you'll have to use WINE). I can't recall a single game that i played more on my Sega than Pirates!
Starting off with a small crew and ship, and a letter that gives you permission to do piratey things, you begin your career by swearing allegiance to a nation. If you are into conquering and plundering, the Spanish might be a good choice...If you are into a more peaceful lifestyle, the trade heavy Dutch might be a better option. Eventually, your sloop can turn into a lean, mean, war-machine, running circles around even the strongest of galleons...or if speed isn't your style, you can commandeer one of those galleons and float around (albeit slowly) in a veritable fortress.
Once you've built a fleet, you can begin to invade ports with your amassed manpower. Land battles operate similar to most turn-based tile strategy games, but these can be avoided if you severely outnumber your enemy. Once you are able to take over ports, you can install governors, and change the balance of power in the region. At this point, you will begin to notice your actions having a much larger affect on the world around you, as nations fall and rise in influence.
Once you've made your mark, you can choose from a number of governor's daughters, and get married, further increasing your reputation in your chosen nation. There are also side quests that lead to you tracking down long lost relatives, battling other notable pirates, and tracking down arch-enemies. You will accumulate more land, and gain in lordly title, and eventually, you can retire. Retiring cashes out you and your crew, and gives you a different ending depending on your accumulated wealth.
As stated above, you can pretty much play Pirates! on anything but a toaster, with recent mobile versions being made available. I still prefer the Sega Genesis version, though, as it is a bit slimmer and less bulky than recent versions.