Democracy

Game Tunnel has a review of Democracy, a politics simulator which allows you to try your hand at governing a well-developed country like the USA. You make policy decisions for economics, social programs, warfare, etc., and try to get elected the following term.

Apparently, although it doesn't refer to a specific country, the political processes are complex and real enough that it's an educational experience to play this game anyway, which might make it a great tool for constructivist learning in a Civics classroom. If nothing else, it would require students to consider many issues they probably have never thought about, and prompt them to think about where to draw the line between practicality and ideology.