  We analyze intermittence and roughening of an elastic interface or domain
wall pinned in a periodic potential, in the presence of random-bond disorder in
(1+1) and (2+1) dimensions. Though the ensemble average behavior is smooth, the
typical behavior of a large sample is intermittent, and does not self-average
to a smooth behavior. Instead, large fluctuations occur in the mean location of
the interface and the onset of interface roughening is via an extensive
fluctuation which leads to a jump in the roughness of order $\lambda$, the
period of the potential. Analytical arguments based on extreme statistics are
given for the number of the minima of the periodicity visited by the interface
and for the roughening cross-over, which is confirmed by extensive exact ground
state calculations.
