If the magnetic field of the Earth suddenly changed, and this DOES happen naturally every 250,000 years or so, the consequences would be fascinating. For life, we can see from the fossil record that the past field changes had no significant effect on living organisms. This is most curious because the field reversal ( North magnetic pole shifting to antarctica and the South magnetic pole shifting to the arctic region in the Northern Hemisphere) one might expect the field to go to zero strength for a century or so. This would let cosmic rays freely penetrate to the Earth's surface and cause mutations. This seems not to have had much effect in the past, so we probably don't really know what is going on during these field reversals. There have been a dozen of them over the last few million years, documented in the rock which has emerged and solidified along the mid-Atlantic Ridge where continental plates are slowly separating. These epochs form parallel bands all long the ridge where the rock has stored a fossilized image of the local orientation of the Earth's magnetic field for the last few million years.
Magnetic field wandering would let the aurora borealis occur at any latitude, but other than that there would be no noticeable effects other than changes in the amount of cosmic rays that penetrate to the ground. Even this effect is minimal because we can visit the Arctic and Antarctic and only receive a slight increase in cosmic rays. So long as the strength of the field remains high during this field wandering event, the effects should be pretty benign.
The Earth's magnetic field is believed to be generated by the rotation of the Earth's molten iron-nickel core. The period of field reversal is determined by the rotation rate of the core and its electrical conductivity. If you were to change either one of these, the field orientation, strength and '250,000 year cycle' would be increased or decreased. We also know from studies of the Sun's magnetic dynamo, that this phenomenon can change abruptly as it did during the 'Little Ice Age' on the Earth a few hundred years ago. There were no sunspots observed on the Sun for 50 years or so, then rather abruptly, the familiar 11-year cycle started-up over the course of a few decades. A similar 'chaotic' phenomenon may occur with the Earth 'suddenly' loosing its magnetic field for a few million years. Already, geophysicists have begun to notice a decline in the strength of the Earth's magnetic field, suggesting that the next field reversal epoch may be about to start. It may, however, take a long time to get here, and we don't really know if the decline is just a natural, ripple, or the portend of something far more sinister.