What can happen if you keep a magnet to your head?

That would depend on the strength of the magnetic field of the magnet.

As magnetic fields can influence electrical current, and our brains work on a massive series of electrical impulses, it's possible that there could be some interaction, but the magnetic field would need to be immense before any noticeable side effects became aparrent.

Magnetic fields are all around us, the earth is basically one big magnet (that's why a needle in a compass points to north) so you could say life on earth is used to exposure to magnetic fields.