We report new L and T dwarfs found in a cross-match of the SDSS Data Release 1 and 2MASS. Our simultaneous search of the two databases effectively allows us to relax the criteria for object detection in either survey and to explore the combined databases to a greater completeness level. We find two new T dwarfs in addition to the 13 already known in the SDSS DR1 footprint. We also identify 22 new candidate and bona-fide L dwarfs, including a new young L2 dwarf and a peculiar L2 dwarf with unusually blue near-IR colors: potentially the result of mildly sub-solar metallicity. These discoveries underscore the utility of simultaneous database cross-correlation in searching for rare objects. Our cross-match completes the census of T dwarfs within the joint SDSS and 2MASS flux limits to the 97% level. Hence, we are able to accurately infer the space density of T dwarfs. We employ Monte Carlo tools to simulate the observed population of SDSS DR1 T dwarfs with 2MASS counterparts and find that the space density of T0-T8 dwarf systems is 0.0070 (-0.0030; +0.0032) per cubic parsec (95% confidence interval), i.e., about one per 140 cubic parsecs. Compared to predictions for the T dwarf space density that depend on various assumptions for the sub-stellar mass function, this result is most consistent with models that assume a flat sub-stellar mass function dN/dM ~ M^0. No >T8 dwarfs were discovered in the present cross-match, though less than one was expected in the limited area (2099 sq. degrees) of SDSS DR1.