I work in pharmaceuticals, though I am not a pharmacist. Note that this is not legal or medical advice; proceed at your own risk. :)
They're right - liquids lose their potency much more quickly than pills. Cough syrup seems to be the one that everyone stores in the back of the cupboard, but it typically loses most of it's effectiveness within a few months of the expiration date. Liquid benadryl is also something that most people keep around the house (it's incredibly helpful for quick reaction on allergic reactions, and if you're far away from a hospital it can give you time to get there...) but it does expire and need replacing relatively often.
Not a medication, but: check the expiration date on your sunscreen. You can get wicked bad sunburns with stuff that's only 2-3 months expired.
Beyond that, I personally push it on drugs where 90% efficacy is perfectly fine with me (pills: advil, tylenol, aleve, migraine medication, allergy meds, etc - I've used all of these several years expired, and they worked as I needed them to). For stuff where I actually depend on the efficacy, though, I'm not willing to push it (birth control pills, EpiPens, and the like). Some things are worth ensuring 100% efficacy. :)