According to The Spice House, if you buy small batches of ground spices, you can use them for 6 months to a year. Whole spices can last 2-3 years. Whole nutmegs can last decades.
To keep spices fresh, store them in airtight containers or sealable plastic bags. put them in a dark and cool place away from the stove and sun.
To check that your spices are fresh, simply give them a smell. If they smell weak or look faded, throw them out and start fresh.