The drug companies are conservative with expiration dates since they can be sued because one of their products did not perform as advertised and because of FDA regulations. Reaching the expiration date doesn't mean the meds become completely useless after that date. That's just the date that the company is comfortable claiming that the product is still stable and fully potent. Drug companies spend a LOT of money doing stability/potency testing of their products. Samples are taken from each manufacturing batch and monitored over time so that unusual degradation in a batch can be detected. Some samples are kept under ideal conditions and others under more adverse conditions.
Some medications, particularly prescription meds, need to perform in a predictable way otherwise they could be dangerous. E.g. an old heart medication tablet could dissolve faster than expected in your body and give you more medication than is safe. Or the pill could "harden" with age and not give you enough of a dose in the expected time frame.
In general, a med will likely still be "good enough" past that date, but as CJK points out, you have no idea what changes have occurred after the expiration. Is one year past OK? Two years? Three? While it may be cost effective for a large hospital chain or the VA to test their med supplies for potency past the expiration date, regular Joe's like us don't have that luxury.