From symmetry arguments we construct a simple Langevin model to describe driven interfaces such as lattice sandpile models composed of discrete grains in the presence of white noise. The model exhibits generic scale invariance (or self-organized criticality) with calculable exponents in all dimensions. For spatial dimensions 1<d2 it undergoes a roughening transition between two distinct phases with algebraic correlations. The transition is Kosterlitz-Thouless-like in d=2. © 1991 The American Physical Society.