Seeds Are Alive!
Seeds are living things, so treat them with care.
Although some seeds can survive extended periods of storage, it is usually better to plant seed sooner rather than later, as germination rates naturally decrease over time. Do not crush or damage them. Do not let your seeds freeze (or overheat) while in storage and make sure they stay dry.
Storage of Seeds
Moisture and heat are the main enemies of viable seed; strong sunlight is inadvisable, too. Cool and dry is the key. Avoid wildly fluctuating temperatures and high humidity. So if one place keeps a more steady temperature (even if it's a tad warmer) then use that space for your seed storage.
As a general rule, temperatures around 4*C (40*F) work well for maintaining long term seed viability. Cool storage keeps seeds fresh as it reduces the rate at which they respire, or 'breathe’.
As most refrigerators are set at 4*C (40*F) they make the ideal storage facility.
Some of the more obscure varieties of seeds may have to be cold stored and some may not store well at all, and need to be planted right away - but MOST seeds are fine if stored this way and should remain viable for a year or two, or even longer.
(Do not keep them in the same compartment with fruits and vegetables as some give off a chemical as they ripen that will inhibit the germination of many species of seed)
Packaging and containers
The best way to store seeds is to package them in paper envelopes or bags since they allow for good air circulation and don't sweat. Seed can also be safely stored in airtight, well-sealed containers, either glass or plastic, with desiccant / silica gel packets to absorb excess moisture. Keep in mind that humidity and lack of air circulation will cause mold, disease and prompt seeds to germinate prematurely.
Reuse the tiny bags of silica gel that come inside new electronics / leather goods.
Dry them for a few minutes at a very low temperature in your oven. If you do not have silica packs, a few grains of dry rice or some powdered milk wrapped in a tissue can also help to absorb moisture.
The best jars for storage are wide mouth mason jars used for canning. They have the proper airtight seal that is essential for long term storage.
Label and date.
Be sure to write the date, name of plant (and perhaps any growing instructions) on the package, or keep the growing instructions in a garden journal or similar. This will come in handy when using the seeds a year or more later, and will be appreciated if you give the seeds to someone else.
Different seeds can be saved for different lengths of time. Viability charts are available via the wonder of the world wide web. They will give you the average number of years certain seeds can be stored.
Parsnip seeds can only be saved for one year. Watermelon seed can be stored for 5 years, Poppies can live in the soil for over fifty years!