We generate theoretical albedo and reflection spectra for a full range of extrasolar giant planet (EGP) models, from Jovian to 51 Pegasi class objects. Our albedo modeling utilizes the latest atomic and molecular cross sections, Mie theory treatment of scattering and absorption by condensates, a variety of particle size distributions, and an extension of the Feautrier technique, which allows for a general treatment of the scattering phase function. We find that, because of qualitative similarities in the compositions and spectra of objects within each of five broad effective temperature ranges, it is natural to establish five representative EGP albedo classes. At low effective temperatures (Teff<~150 K) is a class of ``Jovian'' objects (class I) with tropospheric ammonia clouds. Somewhat warmer class II, or ``water cloud,'' EGPs are primarily affected by condensed H2O. Gaseous methane absorption features are prevalent in both classes. In the absence of nonequilibrium condensates in the upper atmosphere, and with sufficient H2O condensation, class II objects are expected to have the highest visible albedos of any class. When the upper atmosphere of an EGP is too hot for H2O to condense, radiation generally penetrates more deeply. In these objects, designated class III or ``clear'' because of a lack of condensation in the upper atmosphere, absorption lines of the alkali metals, sodium and potassium, lower the albedo significantly throughout the visible. Furthermore, the near-infrared albedo is negligible, primarily because of strong CH4 and H2O molecular absorption and collision-induced absorption (CIA) by H2 molecules. In those EGPs with exceedingly small orbital distance (``roasters'') and 900 K<~Teff<~1500 K (class IV), a tropospheric silicate layer is expected to exist. In all but the hottest (Teff>~1500 K) or lowest gravity roasters, the effect of this silicate layer is likely to be insignificant because of the very strong absorption by sodium and potassium atoms above the layer. The resonance lines of sodium and potassium are expected to be salient features in the reflection spectra of these EGPs. In the absence of nonequilibrium condensates, we find, in contrast to previous studies, that these class IV roasters likely have the lowest visible and Bond albedos of any class, rivaling the lowest albedos of our solar system. For the small fraction of roasters with Teff>~1500 K and/or low surface gravity (<~103 cm s-2 class V), the silicate layer is located very high in the atmosphere, reflecting much of the incident radiation before it can reach the absorbing alkali metals and molecular species. Hence, the class V roasters have much higher albedos than those of class IV. In addition, for class V objects, UV irradiation may result in significant alkali metal ionization, thereby further weakening the alkali metal absorption lines. We derive Bond albedos (AB) and Teff estimates for the full set of known EGPs. A broad range in both values is found, with Teff ranging from ~150 to nearly 1600 K, and AB from ~0.02 to 0.8. We find that variations in particle size distributions and condensation fraction can have large quantitative, or even qualitative, effects on albedo spectra. In general, less condensation, larger particle sizes, and wider size distributions result in lower albedos. We explore the effects of nonequilibrium condensed products of photolysis above or within principal cloud decks. As in Jupiter, such species can lower the UV/blue albedo substantially, even if present in relatively small mixing ratios.