Yes. Pretty much everything expires for one reason or another. For some things an expiration date is of minimal importance and there may not even be one. Adhesives and plastics break down over time (even if stored perfectly). Eventual things will just fall apart and not be useful. Some medications get weaker with time, others become toxic.
For some things without an expiration date, I still replace them. Tourniquets are an example. It is a life safety device. Climbing rope expires in 10 years with perfect storage and no use (5 years if used). I figure the material in a tourniquet breaks down as well, and storage is usually far from perfect as they are carried, exposed to temperature extremes, possibly petroleum fumes, Etc.
Most things should have an expiration date printed on them, if it does not, it either does not expire, or it is so old that they where not required at the time (and I would replace it). At my last job, the boss would never throw anything out and as it was a small facility supply turn over was not very fast for some items. She told me, if it does not have an expiration date, it does not expire and keep it. I found sterile gloves that where so old they had became a single blob in the packaging, catheters that I could pull apart with my finger tips, suture kits from 20 years ago, and dry rotted MAST pants. No one would grab that stuff to use as it looked bad, but no one would throw it out either. I disposed of every bit of it, because if someone had used something like that on my family I would want to give them a Lefort 3 fracture and some other injures, so why the hell would I leave them around to be used on other peoples families.
Playing with the old stuff is a great idea.