  We calculate the critical current $I_c$ across in-plane (001) tilt grain
boundary junctions of high temperature superconductors. We solve for the
electronic states corresponding to the electron-doped cuprates, two slightly
different hole-doped cuprates, and an extremely underdoped hole-doped cuprate
in each half-space, and weakly connect the two half-spaces by either specular
or random quasiparticle tunneling. We treat symmetric, straight, and fully
asymmetric junctions with s-, extended-s-, or d$_{x^2-y^2}$-wave order
parameters. For symmetric junctions with random grain boundary tunneling, our
results are generally in agreement with the Sigrist-Rice form for ideal
junctions that has been used to interpret ``phase-sensitive'' experiments
consisting of such in-plane grain boundary junctions. For specular grain
boundary tunneling across symmetric juncitons, our results depend upon the
Fermi surface topology, but are usually rather consistent with the random facet
model of Tsuei {\it et al.} [Phys. Rev. Lett. {\bf 73}, 593 (1994)]. Our
results for asymmetric junctions of electron-doped cuparates are in agreement
with the Sigrist-Rice form. However, ou resutls for asymmetric junctions of
hole-doped cuprates show that the details of the Fermi surface topology and of
the tunneling processes are both very important, so that the
``phase-sensitive'' experiments based upon the in-plane Josephson junctions are
less definitive than has generally been thought.
