We present results from a survey searching for spatially resolved near-infrared line emission from molecular hydrogen gas in the circumstellar environments of nine young stars: AA Tau, AB Aur, DoAr 21, GG Tau, GM Aur, LkCa 15, LkH 264, UY Aur, and V773 Tau. Prior high-resolution spectra of these stars showed the presence of rovibrational H2 line emission at 2.12 m with characteristics more typical of gas located in protoplanetary disks rather than outflows. In this study, we spatially resolve the H2 emission in the eight stars for which it is detected. LkCa 15 is the only target that exhibits no appreciable H2 despite a prior detection. We find an anticorrelation between H2 and X-ray luminosities, likely indicating that the X-ray ionization process is not the dominant H2 excitation mechanism in these systems. AA Tau, UY Aur, and V773 Tau show discrete knots of H2, as typically associated with shocks in outflowing gas. UY Aur and V773 Tau exhibit spatially resolved velocity structures, while the other systems have spectrally unresolved emission consistent with systemic velocities. V773 Tau exhibits a complex line morphology indicating the presence of multiple excitation mechanisms, including red- and blueshifted bipolar knots of shock-excited outflowing gas. AB Aur, GM Aur, and LkH 264 have centralized yet spatially resolved H2 emission consistent with a disk origin. The H2 images of AB Aur reveal spiral structures within the disk, matching those observed in ALMA CO maps. This survey reveals new insights into the structure and excitation of warm gas in the circumstellar environments of these young stars.