Ticket to Ride was the winner of the 2004 Spiel des Jahres Award, the single most prestigious award world-wide for boardgames. And Alan Moon, its designer, is one of the most highly regarded designers of contemperary boardgames. From its website, the publishers, Days of Wonder, offer a free online-playable version of the game--with some limitations on free players.
It's an excellent game. Playable (like most Eurogames) in less than an hour, it requires careful planning and a bit of luck to succeed. You collect train cards that allow you to claim railway routes, earning points for doing so (and proportionally more for longer routes, which require more cards); you also have some number of "destination tickets", which earn you extra points if your routes link the two cities listed on the card (and cost you points if you fail to link them).
This online version of the game is, in some ways, preferable to the boardgame--the cities you must link light up to remind you, and there's no chance of the cat scattering the pieces to the winds. And of course, there are always people on the servers with which to play--and the online game supports both the North American and European boards.
Although the game is free to play, as a free player you aren't rated and can't start new games, only join ones started by others. If you want to do that, they charge $18/a year--or you can get a year free by buying the boardgame. (Additionally, Skotos subscribers get unlimited free access to the game--you probably wouldn't want to become one just for this game, but if you already subscribe for access to another of their games, it's a nice bonus.)
If you have any interest in quick-play multiplayer online games that require some strategy and planning, give it a whirl.