Using the 8.4 m Large Binocular Telescope, we observed six GRB afterglows from 2.8 hr to 30.8 days after the burst triggers to systematically probe the late-time behaviors of afterglows including jet breaks, flares, and supernova bumps. We detected five afterglows with Sloan r' magnitudes ranging from 23.0 to 26.3 mag. The depth of our observations allows us to extend the temporal baseline for measuring jet breaks by another decade in timescale. We detected two jet breaks and a third candidate, all of which are not detectable without deep, late-time optical observations. In the other three cases, we do not detect the jet breaks either because of contamination from the host galaxy light, the presence of a supernova bump, or the intrinsic faintness of the optical afterglow. This suggests that the basic picture that GRBs are collimated is still valid and that the apparent lack of Swift jet breaks is due to poorly sampled afterglow light curves, particularly at late times.