  For static, spherically symmetric space-times in general relativity (GR), a
no-go theorem is proved: it excludes the existence of wormholes with flat
and/or AdS asymptotic regions on both sides of the throat if the source matter
is isotropic, i.e., the radial and tangential pressures coincide. It explains
why in all previous attempts to build such solutions it was necessary to
introduce boundaries with thin shells that manifestly violate the isotropy of
matter. Under a simple assumption on the behavior of the spherical radius
$r(x)$, we obtain a number of examples of wormholes with isotropic matter and
one or both de Sitter asymptotic regions, allowed by the no-go theorem. We also
obtain twice asymptotically flat wormholes with anisotropic matter, both
symmetric and asymmetric with respect to the throat, under the assumption that
the scalar curvature is zero. These solutions may be on equal grounds
interpreted as those of GR with a traceless stress-energy tensor and as vacuum
solutions in a brane world. For such wormholes, the traversability conditions
and gravitational lensing properties are briefly discussed. As a by-product, we
obtain twice asymptotically flat regular black hole solutions with up to four
Killing horizons. As another by-product, we point out intersection points in
families of integral curves for the function $A(x) = g_{tt}$, parametrized by
its values on the throat.
