  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 dH/dt > 0. Demanding the absence of instabilities in this model
requires dH/dt <~ H^2. 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.
