I've been working on methods for prolonging the shelf life of parmigiano reggiano for a few years now. I'm pretty much a mozzarella purist when it comes to pizza, and, although I use a ton of it in lasagna, I really don't make lasagna much. I like to have PR around, though, so I need to be able to store it for quite some time- at least 6 months and usually around 8.
I was storing it in baggies/ziploc bags, but, over time, the air permeable plastic would slowly drain all the cheese of it's moisture and I'd end up with a rock. You can still cook with it, but grating it is a tremendous PITA, you'll never be able to shred it, it melts strangely, the perceived saltiness goes up, and, imo, the flavor fades. Plastic (including shrinkwrap) is fine for a couple months (maybe), but, beyond that, I'd go with glass.
Glass does have some issues, though. Finding a glass jar that will accommodate your chunk of cheese is tricky. I tend to look for rectangular wedges of cheese that will fit in a 16 oz. peanut butter jar (Smuckers). In a glass jar with either a metal or a thick plastic lid, I can end up with an 8 month old chunk of parm that's identical in taste and consistency to the day that it was purchased.
The other issue with glass is mold. Mold is not the end of the world for hard cheeses. Most food safety experts will tell you to cut it off and the cheese will be fine. At $12.99/lb (the price I pay), I don't like losing cheese, though. In the factory, during the aging process, they wipe off the mold with a cloth. I've tried this a few times without ill effects, but... you have to stay on top it. If you ignore the mold for too long, it will start penetrating the cheese.
My most recent approach has been finding ways to avoid the mold completely. With the last chunk, I added salt to the jar (a couple teaspoons) and tossed it to coat the cheese. Before I used the cheese, I rinsed it off and dried it with a paper towel. No mold, but, the cheese did weep a tiny bit- not enough to affect grate-ability, though, and the flavor was still flawless. I'm still contemplating other methods (some sort of painted on brine, perhaps), but, for the moment, I think I'm going to stick with the salt technique. I highly recommend it.