We have analyzed magnetic field data returned from Mars Global Surveyor (MGS) for signatures of electromagnetic plasma waves upstream from the Martian bow shock. We discuss two recurring wave features in the data. Left-hand polarized waves (0.04--0.10 Hz) observed near the local proton gyrofrequency (PCWs) propagate at small to moderate angles to the magnetic field and have amplitudes that decrease with distance from Mars. They are concentrated in two locations upstream of the Martian shock. PCWs were reported from Phobos 2 observations and can be attributed to solar wind pickup of Mars' hydrogen exosphere. Higher-frequency waves (0.4--2.3 Hz) are observed when MGS is magnetically connected to the Martian shock. These waves have not been reported at Mars before, but have been reported at many solar system bodies, and are attributed to whistler waves generated at the shock and propagating upstream. The sense of polarization (left-handed or right-handed) of the whistler waves observed in the spacecraft frame depends upon the angle between the magnetic field and the solar wind flow direction. The whistler waves at Mars follow the trends in frequency, amplitude, propagation angle, and eccentricity observed at other solar system bodies.