Nikkor serials
The serial number can help you avoid production runs that are known or rumoured to have had problems. Old manual focus Vivitar Series 1 lenses were made by different manufacturers, some held in higher regard than others.
The serial number, if shown in the listing photos, can protect you (and the seller) from substitution with another lens.
I once returned a lens to a well-known dealer which had had the serial number removed and evidence of a poor quality repair. Why should anyone legitimately go to the trouble of removing the serial number?