We have attempted adaptive optics (AO) imaging of planets around nearby stars in the L' and M bands, using the Clio instrument on the MMT. The MMT AO system, with its deformable secondary mirror, offers uniquely low background AO-corrected images in these bands. This allowed us to explore a wavelength regime that has not been well utilized in searches for extrasolar planets, but offers some advantages over the more commonly used shorter-wavelength H band regime. We have taken deep L' and M band images of the interesting debris disk stars Vega and ϵ Eri. Our observations of ϵ Eri attain better sensitivity to low mass planets within 3 arcseconds of the star than any other AO observations to date. At 1.7 arcsec, the maximum separation of the known planet ϵ Eri b, our M band sensitivity corresponds to objects only 9-16 times brighter than the predicted brightness of this planet. M is by far the most promising band for directly imaging this planet for the first time, though Clio would require a multi-night integration. We have carried out a survey of 50 nearby stars, using mostly the L' band. The survey objective was to determine whether power law fits to the statistics of planet mass m and orbital semimajor axis a from radial velocity (RV) surveys apply when extrapolated to orbital radii beyond the outer limits of RV sensitivity. Given dN/dm ~ m^{-1.44}, our survey null result rules out dN/da ~ a^{-0.2} extending beyond 155 AU, or dN/da constant extending beyond 70 AU, at the 95% confidence level. We have not placed as tight constraints on the planet distributions as the best H band surveys. However, we have probed older planet populations and by using a different wavelength regime have helped diversify results against model uncertainties. We have developed careful and well-tested observing, image processing, sensitivity analysis, and source detection methods, and helped advance L' and M band AO astronomy. These wavelengths will become increasingly important with the advent of new giant telescopes sensitive to interesting, low-temperature planets with red H-L' and H-M colors.