The first game is OpenTTD. This is a great game for us who did not get a model railroad when we were kids. OpenTTD is an open source variant of Transport Tycoon Deluxe from the 1990:s.
The aim is to move cargo, mail, and people between cities and factories, and of course to generate profits for your transport company. There are many vehicles to choose from, but trains are by far the best. Building an efficient railroad network with good-looking and optimal intersections is a real challenge. When a city receives good transport service it grows, and getting the cities to grow as large as possible, extending your customer base, is one of the main goals. The game can be a bit stressful when there are hoards of people in each city waiting for your trains (if you're the type to care).
I have played OpenTTD at LAN parties, which is great fun. I prefer cooperative multi player games, in which one can build huge railroad networks together with friends. The MIDI music in the game is great, both the original tunes and the free ones composed for the open version. An active community has grown around the game, with a forum and a wiki. Railway signals, for example, is a complex topic, luckily there is good help in the wiki gameplay manual.
As a bonus, one learns geography when playing scenarios set on real-world maps, such as the town of Urk in the Netherlands on the screen shot above.