  We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with
rectilinear coordinates. Motivated by the analogy of the formalism of the
quantum mechanical harmonic oscillator problem in quantum phase-space with that
of the canonical-type NC 2-D space, and noting that the square of length in the
latter case is analogous to the Hamiltonian in the former case, we arrive at
the conclusion that the length and area are quantized in such an NC space, if
the area is expressed entirely in terms of length. We extend our analysis to
3-D case and formulate a ladder operator approach to the quantization of length
in 3-D space. However, our method does not lend itself to the quantization of
spacetime length in 1+1 and 2+1 Minkowski spacetimes if the noncommutativity
between time and space is considered. If time is taken to commute with spatial
coordinates and the noncommutativity is maintained only among the spatial
coordinates in 2+1 and 3+1 dimensional spacetime, then the quantization of
spatial length is possible in our approach.
