  We prove the vanishing of the bounded cohomology of lamplighter groups for a
wide range of coefficients. This implies the same vanishing for a number of
groups with self-similarity properties, such as Thompson's group F. In
particular, these groups are boundedly acyclic.
  Our method is ergodic and applies to large transformation groups where the
Mather-Matsumoto-Morita method sometimes fails because not all are acyclic in
the usual sense.
