Just about anything! If you can do it on a computer, you can probably do it faster on a computer grid.

Science and research are the first and largest applications so far: grids allow researchers to tackle questions much larger and more difficult than ever before possible.

Other applications include community-centric uses, such as interactive video conferencing, distributed musical concerts, or support for international collaborations all trying to perform complex simulations using detectors located all over the world.

There are also applications in industry, finance, humanities and entertainment.

You can also categorize applications by their general computational nature.