We present adaptive optics data from the Keck telescope, taken while the Huygens probe descended through Titan's atmosphere and on the days following touchdown. No probe entry signal was detected. Our observations span a solar phase angle range from 0.05¿ up to 0.8¿, with the Sun in the west. Contrary to expectations, the east side of Titan's stratosphere was usually brightest. Compiling images obtained with Keck and Gemini over the past few years reveals that the east-west asymmetry can be explained by a combination of the solar phase angle effect and an enhancement in the haze density on Titan's morning hemisphere. While stratospheric haze was prominent over the northern hemisphere, tropospheric haze dominated the south, from the south pole up to latitudes of ~45¿S. At 2.1 ¿m this haze forms a polar cap, while at 1.22 ¿m it appears in the form of a collar at 60¿S. A few small clouds were usually present near the south pole, at altitudes of 30--40 km. Our narrowband J,H,K images of Titan's surface compare extremely well with that obtained by Cassini ISS, down to the small-scale features. The surface contrast between dark and bright areas may be larger at 2 ¿m than at 1.6 and 1.3 ¿m, which would imply that the dark areas may be covered by a coarser-grained frost than the bright regions and/or that there is additional 2 ¿m absorption there.