They may not look like it, but seeds are very much alive. However they don't remain so forever. How long seeds remain viable depends on the type of seed and how well it is stored. To store them for the longest time, be certain they are completely dry, to the point of being brittle, before you pack them away. Then keep them in an air tight container out of direct sunlight. (More tips for storing seeds.)
Here are some average years of viability for well stored vegetable seeds, compiled from regional sources. To be fully certain of your own seeds, you can also do this easy viability test.
Seed Storage Guidelines