  We present detailed calculations of nonthermal synchrotron and synchrotron
self-Compton (SSC) spectra radiated by blast waves that are energized by
interactions with a uniform surrounding medium. Radio, optical, X-ray and
gamma-ray light curves and spectral indices are calculated for a standard
parameter set that yields hard GRB spectra during the prompt emission phase.
Because no lateral spreading of the blast-wave is assumed, the calculated
temporal breaks represent the sharpest breaks possible from collimated outflows
in a uniform surrounding medium. Absence of SSC hardenings in observed GRB
X-ray afterglows indicates magnetic field generation toward equipartition as
the blast wave evolves. EGRET detections of 100 MeV-GeV photons observed
promptly and 90 minutes after GRB 940217 are attributed to nonthermal
synchrotron radiation and SSC emission from a decelerating blast wave,
respectively. The SSC process will produce prompt TeV emission that could be
observed from GRBs with redshifts $z \lesssim 0.1$, provided $\gamma$-$\gamma$
opacity in the source is small. Measurements of the time dependence of the 100
MeV-GeV spectral indices with the planned {\it GLAST} mission will chart the
evolution of the SSC component and test the external shock scenario. Transient
optical and X-ray emissions from misaligned GRBs are generally much weaker than
on-axis emissions produced by dirty and clean fireballs that would themselves
not trigger a GRB detector; thus detection of long wavelength transients not
associated with GRBs will not unambiguously demonstrate GRB beaming.
