The one thing that will make people feel really old, I suspect, is living through three generations of trains on your 'local' network - depending on how frequently the trains are replaced or moved on to other lines. Thinking specifically of cases where a given class spends its whole life on one network, so you get say 30-40 years of service.
Not happened to me yet - the South Western network is what I'd consider 'local' and I've only lived through the CIG/VEPs and 444/450s. Probably won't happen for a while yet, I suspect. (If however one considers the Bournemouth line only, I've already lived through REPs and TCs, 442s, and 444s).
But for someone born in let's say the late fifties, they would have a very good chance of remembering the first-generation EMUs (CORs, BILs, HALs, NOLs, LAVs and the rest), the CIGs and VEPs of course, and the 444s and 450s.
For other lines, which see units replaced more frequently, this could of course happen when you are still in your twenties. If I'd have lived in say Cambridge, for example, I'd have seen at least three generations on London services (loco-hauled diesel, 317s and 365s) well before I'd hit 30.