Considering that I'm a cheesemonger, I'm surprisingly not too discriminating when it comes to old cheese. Admittedly, the quality of a cheese that's been sitting in your fridge will never be superior to its condition upon purchase, but just because a cheese has sat in the back corner of your deli drawer doesn't necessarily mean that it's not fit for consumption.
But just how old is too old?
Always try to consume cheese within a few days of bringing it home. If you're lucky enough to live near a great cheese store, try buying cheeses cut to order in small quantities so that you don't even have to face the dilemma of old cheese.
The best way to tell if a cheese is too old is to taste it. And don't fear. The worst that can happen is that it won't taste great and you can toss it. If it doesn't taste right, it probably isn't. It's natural for a cheese to change in flavor over time, but if it tastes like an entirely different or untasty version of what you first bought, it may have gone bad. Smelling cheese can often be misleading since most cheeses have a natural stink to them, so you have to taste!
Cheese that's been sitting in your refrigerator may take on off flavors, especially if it's wrapped in plastic. Cheeses lose moisture over time, and with this also comes dissipation of flavor. Very old cheeses that are already old (and by that we mean aged) to begin with-- like parm, gouda, or gruyere-- often won't taste like much of anything. Semi-soft cheeses, like washed-rinds, might become softer and stronger tasting. Again, only by tasting will you know if your cheese is past its prime. Trust your palate!
As a rule of thumb, perishability is based on moisture content. A fresh, soft cheese that was made only days before it landed on the shelf will be much more perishable than a cheese that ages for a year before being ready for sale. Fresh cheeses are pretty easy to figure out: If they've spoiled, they'll taste of spoiled or sour milk. Your sense of smell will come in handy with this category of cheese, since fresh cheeses shouldn't smell like much of anything. If they do, they've seen better days. They may also develop patches of blue or pinkish mold.
But don't be afraid of all mold. Mold on harder cheeses can be scraped away to reveal a completely edible and potentially still tasty cheese. For tips on cheese storage, check out The Cheesemonger's Top Ten Rules for Ultimate Cheese Sanity.