  We construct super Yang-Mills theories with extended supersymmetry on
hypercubic lattices of various dimensions keeping one or two supercharges
exactly. Gauge fields are represented by ordinary unitary link variables, and
the exact supercharges are nilpotent up to gauge transformations. Among the
models, we show that the desired continuum theories are obtained without any
fine tuning of parameters for the cases ${\cal N}=2, 4, 8$ in two-dimensions.
