I have always kept my seeds in little zip-lock bags from season to season. Should I really be putting them in the freezer or fridge? It just doesn't seem necessary to me. But then again, I've been wrong before!
Are the seeds you see in packets in the stores refrigerated before they are shipped?
Most of my seeds are from last year. But I have had seeds that have been close to 10 years old, never had a problem. Always just kept em in baggies and in a tupperware.
I save seeds year to year in my fridge, the crisper, not the freezer.
As Mel says, the freezer can cause freezer burn.
I put mine in small plastic baggies or keep the packet they came in and put them in a glass jar with screw-type lids or into a zipper baggy.
Inside the jar or the baggy you need a dessicant, to pull the moisture out of the air. I also toss a few dessicant packs in the crisper drawer itself.
You can make your own dessicant packs by placing a heaping teaspoon of dried milk on two layers of tissue, roll up the tissue one side over the other, then cross the ends one over the other and staple thru those last folded ends so the milk doesn't fall out.
Put one dessicant pack inside each jar and zippered baggy. Change the dessicants every 6 months.
When you are using your seed to start new plants or sow in the garden, keep those in the packet as cool as you can. Keep the packet in the shade outdoors, never in the sunshine. Place the packets back in the fridge as soon as you can. They need to be kept cool to survive.
I've planted 3-yr old peas and they all germinated well. Last year I planted 4-yr old broccoli seeds and other 3-yr old seeds that germinated just fine. Seed life depends on the crop or variety itself, so check the online listings for seed life.
I keep my left over seed in the paper packets that they come in. I fold the edge over, and store them in a cool, dark, place. We actually have a small closet in our garage that I use for my "gardening room." They seem to keep fine in there.
I keep seeds in a cardboard box in the basement. Of course it is dry Utah. The usual relative humidity is around 35-40 %. They have a rather constant temperature of 65-70. Most are in paper. Some in ziploc bags. They seem to keep OK this way.