The list was obtained from the article, "Online Map games to encourage & engages your geographic awareness" in GISUser.com. here is the link to the full article: http://www.gisuser.com/content/view/23043/222/
1. MapDuel: www.mapduel.com
This one may give you a bit of vertigo with all the zooming around, but it is the only one I've found with a question / answer format. It covers the whole globe. I did find one glitch. In a bonus question it asked me, "What is the language of this country?" when it was referring to a U.S. state. Be sure to click on the "Where the hell is Matt?" link too.
2. MapGame: http://www.rethinkingschools.org/just_fun/games/mapgame.html
Not a competitive game but the fact that it focuses on Middle Eastern and Northern Africa countries makes it pertinent to current events in that region.
3. States: http://www.sporcle.com/games/states.php
To win this game you must type in the names of all 50 states in 10 minutes. It places the name of the state that you've just typed in its proper location. Don't forget Alaska and Hawaii (or New Jersey).
4. 50states: http://www.addictinggames.com/50states.html
With this game you have to drag and drop a state shape to where it belongs on a U.S. map. It allows you to get it mostly right via snapping within a certain tolerance. You can compete with others for the best score.