Its rotation produces the magnetic field which keeps the solar wind from stripping away our atmosphere and leaving the Earth a dead planet like Mars. We're getting our money's worth.

Although it's admittedly difficult when the higher temperatures are hundreds or thousands of kilometers away, geothermal power plants do in fact harness that.

If I am not mistaken Iceland uses geothermal to a large extent and is very successful in doing so.

Northern California, as well:

http://en.wikipedia.org/wiki/The_Geysers

Yes, we could use more research in the technical side of that. Right now hard-rock drilling is so expensive that geothermal is only viable where natural circulation of underground water brings heat up from hotter regions.

It's important to note the fact that the heat in the core does not exist in isolation of other fields. The Earth is a dynamo system, and the energy in the core is connected to the planet's magnetic field, the energy bound up in its orbit around the sun, and its gravitational field.