We describe the 44 systems discovered to be within 10 pc of the Sun by the RECONS team, primarily via the long-term astrometry program at the CTIO/SMARTS 0.9 m that began in 1999. The systems-including 41 with red dwarf primaries, 2 white dwarfs, and 1 brown dwarf-have trigonometric parallaxes greater than 100 mas, with errors of 0.4-2.4 mas in all but one case. We provide updated astrometric, photometric (VRIJHK magnitudes), spectral type, and multiplicity information here. Among these are 14 systems that are new entries to the 10 pc sample, including the first parallaxes for 9 systems and new values for 5 systems that had previous parallaxes with errors greater than 10 mas or values placing them beyond 10 pc. We also provide new data for 22 systems known to lie within 10 pc and 9 systems reported to be closer than that horizon but for which new parallaxes place them further away, bringing the total to 75 systems. The 44 systems added by RECONS comprise one of every 7 systems known within 10 pc. We illustrate the evolution of the 10 pc sample from the 191 systems known when the final Yale Parallax Catalog was published in 1995 to the 317 systems known today. Even so close to the Sun, additional discoveries of white, red, and brown dwarfs are possible, both as primaries and secondaries, although we estimate that at least 90% of the stellar systems closer than 10 pc have now been identified.