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They don't have to be hard paper copies but what is wrong with printing them out and filing them with the rest of your paper records? If you don't want to do that you need to be keeping backups offsite either in hard disks or with a backup service. Simply transfer to your back up system.
But to answer your question you do not have to keep hared copies or any copies at all as long as you have the payroll records and can easily reconstruct your W-2's.