I've never seen any disposable diapers state on the packages that they have an expiration date.
Disposable diapers would probably go bad after a period of 10 to 15 years on the shelf but I doubt a parent would keep disposable diapers around that long before they used them since the babies would be out of diapers by then.
I would say that disposable diapers should be good stored in your home for at least a few years so if you have some leftover disposable diapers from one baby or toddler then you could save them for a year or 2 or even 3 years for the next baby without any problem.
I'm sure some of the diapers you buy either in stores or online might sit in warehouses for a few years before they reach you.