The most important thing to remember when storing your seeds is to place them in a location that is cold and dry. The colder and dryer, the better.
Do not subject your seeds to fluctuations in temperature (and humidity), otherwise they will lose their ability to germinate. In other words, do not frequently shuffle your seeds around from room to room, from indoors to outdoors, from near the fireplace to the cold garage, etc.
An underground root cellar is a great example of an excellent storage location. If you are keeping seeds in your home, find a place that is cool, dark, and dry (and where the temperature does not fluctuate much). Do not put them in a greenhouse or a damp woodshed.
Placing your seeds nearer to the floor is better than placing them close to the ceiling where it is warmer.
Even though it might be the coldest spot in your home, do not put your seeds in the refrigerator or freezer unless you have already taken the proper steps to protect them from moisture, like placing them in an airtight container with recharged desiccant.
For now, I am placing my seed packets in airtight opaque canisters with locking clamps and gasket seals (like this) on the floor of my pantry, where the temperature is consistently cool year round. The canisters are ceramic, and I think airtight glass or metal jars would be better, but the ones I already have on hand will do for now. I have been saving small bags of silica gel* desiccant from products that I buy (shoes, electronics, etc.), and have learned that they can be dried out for reuse by placing them in the oven or a dehydrator. The desiccant absorbs moisture and lowers the humidity in the container in which the seeds are stored. I have read that rice can also serve as a desiccant to absorb moisture. I am not too overly concerned about using desiccant since there is relatively low humidity in my home, but if I decide not to bother dehydrating the desiccant, I may throw some rice in the bottom of the canisters that I am using (I figure it can’t hurt). When saving seeds from the garden, I think drying them out becomes a much more complex and necessary process. I may attempt to save my own seeds this year, but at this point I know very little about that particular process from beginning to end. In any case, there are many ideas floating around on the Internet as to ways in which to store seeds (e.g., there are some interesting ideas in this forum thread at Seed Savers Exchange). I’ll be creating a list of ideas that I gather as the season progresses, and will blog about them later on down the road. In the meantime, the book Seed to Seed by Suzanne Ashworth has a great section called Seed Storage Techniques (starting on page 28) for those who save seeds and are serious about storing them (she also covers the steps needed when storing seeds in the refrigerator or freezer).
In his book Growing Vegetables West of the Cascades, master gardener Steve Solomon writes that it is very easy to make your seeds last four times longer than normal. “For the purposes of this book, I define normal storage as being in a cardboard box on a shelf in a closet away from the woodstove, where humidity isn’t excessively high and air temperature tends to be stable. […] More precisely let’s call normal storage 70 degrees F and 70 percent relative humidity (RH). The rule of thumb used in the seed trade is that for every 10 degrees F drop in temperature from normal, combined with a corresponding reduction in humidity that lowers the seed’s moisture content by 1 percent, the life of the seed doubles. It takes roughly a 10 percent drop in relative humidity to lower seed moisture by about 1 percent. So at 60 degrees F/RH60%, the seed life is more or less double the normal span. At 50 degrees F/RH50%, it doubles again to four times normal.” To achieve 50 degreeF/RH50%, he suggests getting a large recharged silica gel packet and placing it in with your seeds in a tightly lidded gallon jar or other airtight container and then keeping it in a cool place such as under the house, in the cellar, or even in cool closet located along a north wall.* Edit: Silica gel is vegan. And according to Rodale's Illustrated Encyclopedia of Organic Gardening (page 123) it is an acceptable form of desiccant. In any case, I might go with the more natural form of rice instead for now. The book Growing Green does not mention anything about silica gel, and simply suggests storing your seeds in a sealed packet in a cool dry place.