Some of the consequences:
Less protection from solar flare
Aurora borealis will be visible across a much greater expanse of earth
Havok for boy scouts, compasses
That last item is worth dwelling on. I actually don't know how long compasses have been in general use -- my talks with Dr. V about sailing and astral navagation suggest at least 200 years... NASA has it... but certainly compasses were one of the indespensible tools of navigation, commerce, warfare, and progress in the past century.
It is fortunate now that we have GPS technology and have progressed beyond the reliance of earth's magnetic field. So consider: our civilization needed a 100+ year period of reliance on earth's magnetic field -- which is not available ~ 1000 years out of every 200k... Would we have progressed to GPS without a magnetic field? How would aerospace tech have advanced to that point without it? Put another way, the GPS network was launched and administered by the Air Force, and the air force wouldn't exist without compasses.
Would Oersted have discovered electromagnetism without having a compass near his electricity demo? Would engineers and scientists have detected a much weaker and less reliable magnetic field, and just found a way to work around it? Would we look at old magnetic rocks of various orientations and wonder, why did they solidify that way? I don't know, but I'm ready to add "functioning magnetosphere" to the list of physical properties of the world that needed to break our way for civilization to progress the way it did. Other things on the list: water, wood, coal, a preponderance of domesticable animals in Europe, etc.
In the past few decades it's become clear that meteors wreak havok with much of life on earth on a regular basis (on the scale of hundreds of millions of years, and getting rarer). It's also clear we're advancing to the point where meteors will no longer be a mortal threat (see "Armageddon", 1998). But it's worth considering a less catastrophic, more melancholy fate: world civilizations stuck in place, unable to easily explore and reliably travel long distances, all the while dazzled by the nightly not-so-northern lights...
Also worth thinking about is if we're not already stuck due to some cosmic coincidence -- ie, the raw materials for cold fusion used to be lying around everywhere but dried up a few hundred years ago.