It's a good idea, if you start your own seeds, to do a thorough cleaning out of the seed supply every year. Keeping old seed around will just lead to frustration. Here is a basic guideline for seed shelf-life:

1 year: onions, parsnips, parsley, salsify, scorzonera, and spinach;
2 years: corn, peas, beans, chives, okra, dandelion;
3 years: carrots, leeks, asparagus, turnips, rutabagas;
4 years: peppers, chard, pumpkins, squash, watermelons, basil, artichokes and cardoons;
5 years: most brassicas, beets, tomatoes, eggplant, cucumbers, muskmelons, celery, celeriac, lettuce, endive, chicory.

I am never too sure about what to do with old seeds. Sometimes I throw them around on bare patches of earth to see what will come up and other times I sadly throw them into the compost or trash. Most importantly, I try to be really careful to order only what I can use within the lifetime of the seed.