Orbiter is a free Space Flight Simulator for Windows. It is not a web app, but must be downloaded and installed on your computer.
With Orbiter, you can launch and fly the space shuttle. It launches from Kennedy Space Center and then you fly it to rendezvous with the International Space Stations. You can also fly Mercury, Gemini, Apollo, Vostok and other spacecraft, including your own design or designs others have made.
The simulator is very realistic and allows you to fly spacecraft, design your own craft, plan interplanetary missions, and learn about space flight and orbital mechanics in a fun way.
This is a great resource for science classes, especially Physical Science, Astronomy, and Physics.
Here are some screen shots from Orbiter:
I plan on using this with my Physics classes as part of their end-of-the year rockets project.