Granny, Robin, and Ed posted on how they store their seeds. So I figured I'd weigh in. Currently I have five containers of seeds. The containers I use are airtight. The two above are stored in the back of the fridge. This tends to keep the seed viable for long periods of time (just make sure to bring the seeds to room temperature before opening). I also have a container in the freezer for seed I might want to use some year, but I'm not this year. Sometimes I find it hard to throw away seed that I've loved but have something else I'm growing now.
These containers are indexed. One has all my big seeds like corn, peas, and beans. The other has everything else. I had these containers for a long time not being used. Then I found out they were the exact size of a seed packet on its side. They are the perfect seed storage containers (2qt ClickClack containers).
The other two are sometimes used. One has seed that will be sown in the garden soon (peas, spinach, lettuce, Asian greens, and fava beans). It is kept by the back door. The other has seed that will be sown indoors soon and is kept upstairs in the plant nursery.