1 - tranportations traffic controlers. All processes must run in real time without any kind of competition for processor to avoid accidents. example: air controlers and train track controlers.
2 - industrial control quality systems. In some cases millions of "objects" must be tested and processed in real-time to avoid delays and failures on the production process.
3 - Artificial intelligence systems. in this case the processement almost always need very fast processement. One example could be a chess game to compete with a human champion :)