I have been poking around Marc Prensky’s Social Impact Games website, browing through the games. Many are just descriptions of games that are in development or that have been developed but are not free or web-based. For instance, in his book Prensky talks about The Monkey Wrench Conspiracy, a game used to teach engineers how to use a new 3D CAD program.
But there are several that are available to try out:

MassBalance: This is a simulation that asks the user to balance the Massachusetts state budget. The game warns you when your budget cuts are dangerous, and you can also raise taxes. Pretty realistic and shows the complicated nature of balancing budgets. (Listed under Public Policy Games)

Kinetic City: This series of games was created by the American Association for the Advancement of Science, based on a National Science Foundation grant. It is an interesting mix of online and offline activities.

Brain Connection: Billed as brain teasers, these online activities help with phonemic awareness and other early literacy skills including sound discrimination.

Team Up: From Girls Inc, a game that emphasizes team building. Each girl has her own strengths and they have to work together to move to new levels.

Girls seem to be a big concern of game designers. Here’s one that’s still under development:

Rapunsel: A constructionist site that hopes to encourage girls to become computer programmers. Rapunsel stands for Real Time Applied Programming for Underrepresented Students’ Early Literacy. So, here’s a game with social concern as a basis for its creation.