UMapper GeoDart is an easy way to make your own geography trivia games. They plug into a bunch of different map APIs like Google and Bing which you can then use via a WYSIWYG interface to create map trivia games. You can create the games using their Flash client and then the map games publish out as Flash games which means you can embed them around the web. One other interesting thing they included was an Export To Actionscript button which gives you all the AS3 source code you would need to include that exact same map you just built into your own Flash game. Because the output for these games is in Flash you can also play them on Android devices but they also appear to have an HTML5 version which is embedable via an IFRAME.
Using their game creator (which looks like it is built in Flex) you basically drag and drop points on a map and then you add names to those points and a question in the description field for that point. The game client will then ask that question of the user and it is up to the user to click on the map and find the point that the question asked about (an example would be Where is London? and then the user has to click in London on the world map to answer it correctly). You have a limited amount of time to answer each question (which is configurable). The closer on the map to the correct answer the more points you receive. If you are looking to create a more interactive arcade style game you might build your own game using Pulado.
Head over to UMapper GeoDart and start building your own geography trivia games by clicking here.