I'm a long-time fan of the Oregon Trail computer game (and I've been thinking about all things Oregon Trail lately). I remember first encountering the game on an Apple IIe computer during the second grade -- it fascinated me. Why did my oxen keep dying? How come people kept getting dysentery and breaking their legs? Why can't I just play this game all day?! In later years, I bought an Apple IIgs for the sole purpose of playing Oregon Trail. It didn't fascinate me quite as much, though it did bring back memories.
Good old Wikipedia brings us a complete history of The Oregon Trail. The game was originally developed in the early 70's, designed for use in a history class one of the developers was teaching. After the initial release, development moved to the Minnesota Educational Computing Consortium (MECC), which was a rather interesting state agency that eventually produced a bunch of educational software.
The game itself guides the player through a virtual trip down the Oregon Trail, starting with provisioning the wagon, selecting the party members, and then setting out on the journey. You could choose to play the game as a banker, a carpenter, or a farmer -- this affected how much money you started out with, and thus the difficulty of the game. (If you completed the game as the farmer, which was completely impossible for me in the second grade, you'd get an extra-high score at the end.)
You can read more at Wikipedia, but there are a variety of other excellent Oregon Trail resources on the web. Gaming Our Way Through History discusses the game from an educator's perspective. The Educational Software Classics site has detailed info on the game's creators, the game's innovations, and some screenshots (scroll down). Finally, if you're on Windows and running Firefox, you can Play Oregon Trail on VirtualApple. The rest of us can try out Westward Trail, a web-based Oregon Trail clone with updated graphics.