|MadSci Network: Astronomy|
If the Earth's magnetic field disappeared, more particles from the Sun and from the cosmic radiation would reach the surface. At the moment, many particles can reach the surface at the Poles because the field is vertical there so the particles quite easily make it down along the field lines to the surface. Near the equator the particles are scattered away from Earth by the horizontal field lines.
Therefore, if the field disappeared altogether I think conditions would be like they are now near the poles, all over Earth. There would be plenty of something like aurora, but aurora depends on field lines for making the wavy curtains so I guess there would be more of an even glow, in the absence of a magnetic field. The glow would be very weak, though, because the magnetic fields are needed to trap the particles to keep the glow going.
The oceans and the atmsophere would not boil away. We know that because the field does disappear every now and then! The field reverses its polarity and for a while there is no field, and then it returns with opposite polarity. This has happened many times - the evidence is frozen in magnetic fields in rocks that form from the molten state.
Try the links in the MadSci Library for more information on Astronomy.