  We generate scalar thick brane configurations in a 5D Riemannian space time
which describes gravity coupled to a self-interacting scalar field. We also
show that 4D gravity can be localized on a thick brane which does not
necessarily respect Z_2-symmetry, generalizing several previous models based on
the Randall-Sundrum system and avoiding the restriction to orbifold geometries
as well as the introduction of the branes in the action by hand. We begin by
obtaining a smooth brane configuration that preserves 4D Poincar'e invariance
and violates reflection symmetry along the fifth dimension. The extra dimension
can have either compact or extended topology, depending on the values of the
parameters of the solution. In the non-compact case, our field configuration
represents a thick brane with positive energy density centered at y=c_2,
whereas in the compact case we get pairs of thick branes. We recast as well the
wave equations of the transverse traceless modes of the linear fluctuations of
the classical solution into a Schroedinger's equation form with a volcano
potential of finite bottom. We solve Schroedinger equation for the massless
zero mode m^2=0 and obtain a single bound wave function which represents a
stable 4D graviton and is free of tachyonic modes with m^2<0. We also get a
continuum spectrum of Kaluza-Klein (KK) states with m^2>0 that are suppressed
at y=c_2 and turn asymptotically into plane waves. We found a particular case
in which the Schroedinger equation can be solved for all m^2>0, giving us the
opportunity of studying analytically the massive modes of the spectrum of KK
excitations, a rare fact when considering thick brane configurations.
