We calculate self-consistent extrasolar giant planet (EGP) phase functions and light curves for orbital distances ranging from 0.2 to 15 AU. We explore the dependence on wavelength, cloud condensation, and Keplerian orbital elements. We find that the light curves of EGPs depend strongly on wavelength, the presence of clouds, and cloud particle sizes. Furthermore, the optical and infrared colors of most EGPs are phase-dependent, tending to be reddest at crescent phases in V - R and R - I. Assuming circular orbits, we find that at optical wavelengths most EGPs are 3-4 times brighter near full phase than near greatest elongation for highly inclined (i.e., close to edge-on) orbits. Furthermore, we show that the planet/star flux ratios depend strongly on the Keplerian elements of the orbit, particularly inclination and eccentricity. Given a sufficiently eccentric orbit, an EGP's atmosphere may make periodic transitions from cloudy to cloud-free, an effect that may be reflected in the shape and magnitude of the planet's light curve. Such elliptical orbits also introduce an offset between the time of the planet's light-curve maximum and the time of full planetary phase, and for some sets of orbital parameters, this light-curve maximum can be a steeply increasing function of eccentricity. We investigate the detectability of EGPs by proposed space-based direct-imaging instruments.