A grid of coupled qubits can be used to simulate quantum systems. A quantum system many physicists like to simulate is the Hubbard model (http://en.wikipedia.org/wiki/Hubbard_model) . A simulation of the Hubbard model can possibly lead to a better understanding of high temperature superconductivity. This in turn can tell physicists where to look for room-temperature superconductors, the discovery of which will drastically transform the world as we know it.

This is in my opinion the most important application of a quantum computer.