The disks of spiral galaxies are commonly thought to be truncated: the radial surface brightness profile steepens sharply beyond a certain radius (3-5 inner disk scale lengths). Here we present the radial brightness profiles of a number of barred S0-Sb galaxies with the opposite behavior: their outer profiles are distinctly shallower in slope than the main disk profile. We term these "antitruncations"; they are found in at least 25% of a larger sample of barred S0-Sb galaxies. There are two distinct types of antitruncations. About one-third show a fairly gradual transition and outer isophotes that are progressively rounder than the main disk isophotes, suggestive of a disk embedded within a more spheroidal outer zone--either the outer extent of the bulge or a separate stellar halo. But the majority of the profiles have rather sharp surface brightness transitions to the shallower, outer exponential profile and, crucially, outer isophotes that are not significantly rounder than the main disk; in the Sab-Sb galaxies, the outer isophotes include visible spiral arms. This suggests that the outer light is still part of the disk. A subset of these profiles are in galaxies with asymmetric outer isophotes (lopsided or one-armed spirals), suggesting that interactions may be responsible for at least some of the disklike antitruncations.