  We investigate noncommutative deformations of quantum field theories for
different star products, particularly emphasizing the locality properties and
the regularity of the deformed fields. Using functional analysis methods, we
describe the basic structural features of the vacuum expectation values of
star-modified products of fields and field commutators. As an alternative to
microcausality, we introduce a notion of $\theta$-locality, where $\theta$ is
the noncommutativity parameter. We also analyze the conditions for the
convergence and continuity of star products and define the function algebra
that is most suitable for the Moyal and Wick-Voros products. This algebra
corresponds to the concept of strict deformation quantization and is a useful
tool for constructing quantum field theories on a noncommutative space-time.
