  We consider the problem of enumerating spanning trees on lattices.
Closed-form expressions are obtained for the spanning tree generating function
for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under
free, periodic, and a combination of free and periodic boundary conditions.
Results are also obtained for a simple quartic net embedded on two
non-orientable surfaces, a Moebius strip and the Klein bottle. Our results are
based on the use of a formula expressing the spanning tree generating function
in terms of the eigenvalues of an associated tree matrix. An elementary
derivation of this formula is given.
