  We show that field theories with light-like noncommutativity, that is with
$\theta^{0i}=-\theta^{1i}$, are unitary quantum theories, and that they can be
obtained as decoupled field theory limits of string theory with D-branes in a
background NS-NS $B$ field. For general noncommutativity parameters, we show
that noncommutative field theories which are unitary can be obtained as
decoupled field theory limits of string theory, while those that are not
unitary cannot be obtained from string theory because massive open strings do
not decouple. We study the different theories with light-like noncommutativity
which arise from Type II D-branes. The decoupling limit of the D4-brane seems
to lead to a noncommutative field theory deformation of the $(2,0)$ SCFT of
M5-branes, while the D5-brane case leads to a noncommutative variation of
``little string theories''. We discuss the DLCQ description of these theories.
