Direct observations of cosmic photon spectra from neutralino annihilation at energies above EGRET data might reveal the presence of weakly interacting massive particle (WIMP) dark matter in the Universe. Calculations of the rates for the continuum γ channel and γ-ray line are reviewed. Both the continuum γ-ray spectrum and the γ-ray line arising from neutralino annihilation are studied. Flux estimates are inherently model-dependent; they suffer from uncertainties due to the large allowed ranges in supersymmetrical parameter-space and from a variety of astrophysical models of the dark matter halo profiles. Our analysis allows detection predictions for orbital and ground-based experiments. As an application, we investigate the number of signal events expected to be detected in an orbital experiment (AMS-02) and we make a comparison with atmospheric Cerenkov telescopes.