[en] We present a consistent effective theory that violates the null energy condition (NEC) without developing any instabilities or other pathological features. The model is the ghost condensate with the global shift symmetry softly broken by a potential. We show that this system can drive a cosmological expansion with H-dot > 0. Demanding the absence of instabilities in this model requires H-dot or approx. H². We then construct a general low-energy effective theory that describes scalar fluctuations about an arbitrary FRW background, and argue that the qualitative features found in our model are very general for stable systems that violate the NEC. Violating the NEC allows dramatically non- standard cosmological histories. To illustrate this, we construct an explicit model in which the expansion of our universe originates from an asymptotically flat state in the past, smoothing out the big-bang singularity within control of a low- energy effective theory. This gives an interesting alternative to standard inflation for solving the horizon problem. We also construct models in which the present acceleration has w < -1; a periodic ever-expanding universe; and a model with a smooth 'bounce' connecting a contracting and expanding phase. (author)