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Astrometric measurements for 25 red dwarf systems are presented, includingthe first definitive trigonometric parallaxes for 20 systems within 10 pc ofthe Sun, the horizon of the RECONS sample. The three nearest systems that hadno previous trigonometric parallaxes (other than perhaps rough preliminaryefforts) are SO 0253+1652 (3.84 +/- 0.04 pc, the 23rd nearest system), SCR1845-6357 AB (3.85 +/- 0.02 pc, 24th), and LHS 1723 (5.32 +/- 0.04 pc, 56th).In total, seven of the systems reported here rank among the nearest 100 stellarsystems. Supporting photometric and spectroscopic observations have been madeto provide full characterization of the systems, including complete VRIJHKphotometry and spectral types. A study of the variability of 27 targets revealssix obvious variable stars, including GJ 1207, for which we observed a flareevent in the V band that caused it to brighten by 1.7 mag.  Improved parallaxes for GJ 54 AB and GJ 1061, both important members of the10 pc sample, are also reported. Definitive parallaxes for GJ 1001 A, GJ 633,and GJ 2130 ABC, all of which have been reported to be within 10 pc, indicatethat they are beyond 10 pc. From the analysis of systems with (previously) hightrigonometric parallax errors, we conclude that parallaxes with errors inexcess of 10 mas are insufficiently reliable for inclusion in the RECONSsample. The cumulative total of new additions to the 10 pc sample since 2000 isnow 34 systems -- 28 by the RECONS team and six by other groups. This totalrepresents a net increase of 16% in the number of stellar systems reliablyknown to be nearer than 10 pc.Comment: 33 pages, including 3 figures and 3 table

The Solar Neighborhood. XVII. Parallax Results from the CTIOPI 0.9 m Program: 20 New Members of the RECONS 10 Parsec Sample