Spectroscopy of High-Redshift Supernovae from the ESSENCE Project: The First 2 YearsBased in part on observations obtained at the Cerro Tololo Inter-American Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under a cooperative agreement with the National Science Foundation (NSF); the European Southern Observatory, Chile (ESO Programme 170.A-0519); the Gemini Observatory, which is operated by AURA under a cooperative agreement with the NSF on behalf of the Gemini partnership (the NSF [United States], the Particle Physics and Astronomy Research Council [United Kingdom], the National Research Council [Canada], CONICYT [Chile], the Australian Research Council [Australia], CNPq [Brazil], and CONICET [Argentina] [programs GN-2002B-Q-14, GN-2003B-Q-14, and GS-2003B-Q-11]); the Magellan Telescopes at Las Campanas Observatory; the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona; and the F. L. Whipple Observatory, which is operated by the Smithsonian Astrophysical Observatory. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration; the Observatory was made possible by the generous financial support of the W. M. Keck Foundation.