Hay that has been properly harvested and baled, and has been stored properly, will last for several years in the bale.
Bales that have been opened are best stored at room temperature or cooler in a dry location out of sunlight. We recommend placing 6 mm plastic on the floor of your storage location, pallets on top of the plastic, then the hay on top of the pallets.
While it is not a good idea to just lay a piece of plastic or a tarp over the top of hay (moisture will condense on the bottom side of the plastic and saturate your hay causing it to degrade), it can be a good idea to "tent" plastic over your hay supply if you have any moisture issues from your roof or if you have a particularly dusty storage area. The operative word here is "tent" the plastic so as to cover the hay while allowing airflow around the hay.
It is particularly important in high-humidity areas, such as Western Washington, to have air frequently circulating in your storage area (fans can be placed strategically and turned on for short periods of time) to reduce the chance of growth of "storage mold" on the outside or exposed areas of the bales. Stagnant humid air can cause the growth of storage mold on the exposed areas of the bales, especially during the winter months when humidity is high and air-circulation is low. Running a fan occasionally can be relatively inexpensive insurance on your hay investment.
If you have small animals and purchase a few bales at a time, a garbage can or other similar storage container works well as they are not airtight but do shield your hay from sunlight, which can leach nutrients. Your hay needs to breathe as it naturally has a moisture content (even when cured and baled properly) that, when enclosed in an airtight or sealed bag or container, can cause the growth of mold. Do not store your hay in sealed plastic bags.