Like other Arduino boards, the on-board regulator is rated for an input voltage as high as 20V, even though the recommended input limit is 12V. Being that this is a switching regulator, some might feel safer about going higher than 12V since the regulator is generating less heat / waiting power when compared to previous boards.
the previous Arduino boards, the input capacitors on the Due are only rated for 16V. Since it is an Aluminum Electrolytic, it probably won't fail immediately with >16V applied, however, its lifetime will be compromised.
The hardware page
should list the input limit at 16V, not 20V.