  A ring is rigid if there is no nonzero locally nilpotent derivation on it. In
terms of algebraic geometry, a rigid coordinate ring corresponds to an
algebraic affine variety which does not allow any nontrivial algebraic additive
group action. Even though it is thought that "generic" rings are rigid, it is
far from trivial to show that a ring is rigid. In this paper we provide several
examples of rigid rings and we outline two general strategies to help determine
if a ring is rigid, which we call "parametrization techniques" and "filtration
techniques". We provide many little tools and lemmas which may be useful in
other situations. Also, we point out some pitfalls to beware when using these
techniques. Finally, we give some reasonably simple hypersurfaces for which the
question of rigidity remains unsettled.
