We report on work to increase the number of well-measured Type Ia supernovae (SNe Ia) at high redshifts. Light curves, including high signal-to-noise Hubble Space Telescope data, and spectra of six SNe Ia that were discovered during 2001, are presented. Additionally, for the two SNe with z>1, we present ground-based J-band photometry from Gemini and the Very Large Telescope. These are among the most distant SNe Ia for which ground-based near-IR observations have been obtained. We add these six SNe Ia together with other data sets that have recently become available in the literature to the Union compilation. We have made a number of refinements to the Union analysis chain, the most important ones being the refitting of all light curves with the SALT2 fitter and an improved handling of systematic errors. We call this new compilation, consisting of 557 SNe, the Union2 compilation.