We use squids whenever we need to make very accurate measurements of magnetic fields. Neurologists use them to detect the magnetic field created by the brain neuronal activity. This is called magnetoencephalography.
Physicists often have to measure the magnetic properties of the compounds they study. Accurate measurements of the magnetism of a compound enable to understand better the behaviour of its electrons. Some firms have marketed squids adapted to the needs of laboratories and that are used everywhere around the world. For instance, the accurate studies that enabled these devices were very important to understand new superconductors, their magnetism and the differences they have with new superconductors. Superconductivity enables the study of superconductivity !
Magnetism of an MgB2 sample in presence of a 2-millitesla magnetic field. The susceptibility quickly drops to -1 below 39 K, showing the expulsion of the magnetic field.
Finally, other fields also use squids, such as geology and archaeology.