I buy new ones every year. In the past I would keep some around from one season to the next, but not anymore. When I would keep them from one season to the next, I would rinse with mouthwash, and leave them in the fridge with the reeds separated.
They're just so cheap, though, and I get to support some call makers each year, even if it's just a little, when I buy replacements. I just prefer not to have to worry about taking care of them in the off season.