  We find broad classes of solutions to the field equations for d-dimensional
gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field
with non-vanishing potential. Our construction generates these configurations
from the solution of a single nonlinear ordinary differential equation, whose
form depends on the scalar potential. For an exponential potential we find
solutions corresponding to brane geometries, generalizing the black p-branes
and S-branes known for the case of vanishing potential. These geometries are
singular at the origin with up to two (regular) horizons. Their asymptotic
behaviour depends on the parameters of the model. When the singularity has
negative tension or the cosmological constant is positive we find
time-dependent configurations describing accelerating universes. Special cases
give explicit brane geometries for (compact and non-compact) gauged
supergravities in various dimensions, as well as for massive 10D supergravity,
and we discuss their interrelation. Some examples lift to give new solutions to
10D supergravity. Limiting cases with a domain wall structure preserve part of
the supersymmetries of the vacuum. We also consider more general potentials,
including sums of exponentials. Exact solutions are found for these with up to
three horizons, having potentially interesting cosmological interpretation. We
give several additional examples which illustrate the power of our techniques.
