Supernova (SN) 2006gy was a hydrogen-rich core-collapse SN that remains one of the most luminous optical supernovae ever observed. The total energy budget (> 2 x 10^51 erg radiated in the optical alone) poses many challenges for standard SN theory. We present new ground-based near-infrared (NIR) observations of SN 2006gy, as well as a single epoch of Hubble Space Telescope (HST) imaging obtained more than two years after the explosion. Our NIR data taken around peak optical emission show an

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... ution that is largely consistent with a cooling blackbody, with tentative evidence for a growing NIR excess starting at day ~100. Our late-time Keck adaptive optics (AO) NIR image, taken on day 723, shows little change from previous NIR observations taken around day 400. Furthermore, the optical HST observations show a reduced decline rate after day 400, and the SN is bluer on day 810 than it was at peak. This late-time decline is inconsistent with Co56 decay, and thus is problematic for the various pair-instability SN models used to explain the nature of SN 2006gy. The slow decline of the NIR emission can be explained with a light echo, and we confirm that the late-time NIR excess is the result of a massive (>10 Msun) dusty shell heated by the SN peak luminosity. The late-time optical observations require the existence of a scattered light echo, which may be generated by the same dust that contributes to the NIR echo. Both the NIR and optical echoes originate in the proximity of the progenitor, ~10^18 cm for the NIR echo and <~10-40 pc for the optical echo, which provides further evidence that the progenitor of SN 2006gy was a very massive star.