The "Best before" date is the manufacturer's recommendation based on both quality and food safety. They think the cup quality will deteriorate significantly after that date, and they do not want consumers to have a poor taste experience. Stale coffee is not great for brand image (although manufacturers do not have a unified concept of how high their banner should be held). The product is generally food-safe beyond the best before date. Manufacturers tend to "pad" the dates to be cautious and to avoid liabillity over food safety issues. Improper storage (such as direct sunlight) could shorten product shelf life below expectations.
Coffee is less susceptible to "expiring" (like dairy products for instance). The coffee does go flat and stale inside the package. It is still drinkable when it gets stale. In some stores and households all the coffee is stale already - even though the date code may or may not have passed. While some specialty roasters sell their inventory within a few days of roasting, many manufacturers date code their product for 3 months, 6 months, 12 months or even two or more years from roast date. Keurig's initial date code recommendation was six months, and I believe most of the roasters packaging K-cups still follow 6 month coding (your particular manufacturer will likely verify their standard if you call them).
The K-cup is an exceptionally airtight package and they are nitrogen flushed during the filling process, so the product inside is well protected from oxidation which is one of the most noticeable factors contributing to staling. Therefore the k-cups frequently produce a better tasting cup compared to the same product packed in a lesser packaging type of the same age.
Coffee isn't milk, fortunately. It certainly is not a health issue.
There is a lot of slack in the expiration dates. There are 6 and 9 month expiration dates on k-cups that I am aware of. There is no rhyme or reason to it - so if you see a 6 month k-cup, you're probably good for another 3 months minimum.
Over a long time, the oils in the coffee may turn rancid. That will make it taste more like commerical grade coffee. Some people actually like that, because the coffee tastes stronger. Not better, just stronger, and some people don't know the difference.
Try it, let your taste buds decide. let us know what you find out.