radiation - Earth's magnetic field shields us... from what threat?

This is a nice artistic picture of the magnet field of the earth, shielding us from the solar wind. (source)

Wherever you look, it is stated that without our shield, life would not be possible on earth. The movie "The Core" exaggerates this and shows a gamma-laser-ray melting the Golden Gate Bridge, when the core of the earth stops rotating and the field collapses.

So, we should be very lucky to have the magnetic field protecting us. Shouldn't we?

Wikipedia states that solar wind consists mainly of protons, electrons and alpha particles, in the energy range of 1.5-10keV.

Later, sporadic velocities in a range right below 1000km/s are mentioned, which are still in that energy range.

Alpha particles of that energy have a range of not more than 10cm in air (at ground level). Protons and electrons have a larger range, but still, it's not more than a few meters. So, the air above our heads should be sufficient to protect us from solar wind.

Also, some of the solar wind reaches our atmosphere and generated colourful polar lights, but there seems to be no concern about their hazardousness.

It seems that solar wind is too weak to reach the ground. The energy range also is too low to generate radioactive isotopes.

Cosmic radiation of much higher energy isn't shielded, but even there, we just get some muons (and neutrinos) down here.

So, what's the threat the magnetic field protects us from?

Answer

Actually, in a large solar flare particle energies can get up to 1 GeV, but the top energy of some particles is not really the issue. The issue is the flux of these high energy particles. A 10 MeV proton or electron pretty much rips through most spacecraft bodies, thus, their electronics are effectively exposed to particles at these energies.

The often associated coronal mass ejections (CMEs) produced in association with large solar flares carry with them enhanced fluxes of >MeV protons and electrons. These blobs of plasma and magnetic fields compress the Earth's magnetic field, which can induce DC currents in our power grids and expose geosynchronous (or GPS, I forget which orbit at the co-rotating altitude) spacecraft to the high levels of radiation. After the CME has passed, the effects are not over as they often induce a geomagnetic storm, which enhances the radiation belts and thus further exposes co-rotating spacecraft to high energy particles (thus the name "killer electrons" for the outer radiation belts).

I will add more later and include some links, but the point is that our magnetic field does a tremendous amount to prevent our lives from becoming incredibly complicated, as Timaeus eluded to.

Updated Version
Actually, in a large solar flare particle energies can get up to 1 GeV, but the top energy of some particles is not really the issue. The issue is the flux of these high energy particles. A 10 MeV proton or electron pretty much rips through most spacecraft bodies, thus, their electronics are effectively exposed to particles at these energies.

The often associated coronal mass ejections (CMEs) produced in association with large solar flares carry with them enhanced fluxes of >MeV protons and electrons. These blobs of plasma and magnetic fields compress the Earth's magnetic field, which can induce DC currents in our power grids and expose geosynchronous (or GPS, I forget which orbit at the co-rotating altitude) spacecraft to the high levels of radiation. After the CME has passed, the effects are not over as they often induce a geomagnetic storm, which enhances the radiation belts and thus further exposes co-rotating spacecraft to high energy particles (thus the name "killer electrons" for the outer radiation belts).

The Earth's magnetic field also helps protect our atmosphere from ionizing erosion. By that I mean that once an atom is ionized and exposed to the bulk flow of the solar wind, it will experience a conductive electric field ($\mathbf{E} = -\mathbf{V} \times \mathbf{B}$) and react like a pick-up ion. The force on the particle from such an electric field can easily exceed the gravitational force, thus freeing the particle from the atmosphere. Without the Earth's magnetic field, the ionized part of the upper atmosphere, called the ionosphere, would increase due to the addition of the solar wind's ionization effects. Currently, only charged particles with energies >10-100 MeV, neutral neutrons, or high energy photons (e.g., UV, X-rays, and/or $\gamma$-rays) are able to reach our atmosphere and contribute to the overall ionization.

It is doubtful that during a pole flip of the Earth's magnetic field that we would completely lose our atmosphere, considering several pole flips have happened in the past. However, the point is that our magnetic field does a tremendous amount to prevent our lives from becoming incredibly complicated, as Timaeus eluded to.