We report the discovery of ten transiting extrasolar planets by the HATSouth survey. The planets range in mass from the Super-Neptune HATS-62b, with $M_{p} < 0.179 M_{J}$, to the Super-Jupiter HATS-66b, with $M_{p} = 5.33 M_{J}$, and in size from the Saturn HATS-69b, with $R_{p} = 0.94 R_{J}$, to the inflated Jupiter HATS-67b, with $R_{p} = 1.69 R_{J}$. The planets have orbital periods between 1.6092 days (HATS-67b) and 7.8180 days (HATS-61b). The hosts are dwarf stars with masses ranging from $0.89 M_{odot}$ (HATS-69) to $1.56 M_{odot}$ (HATS-64), and have apparent magnitudes between $V = 12.276 pm 0.020$ mag (HATS-68) and $V = 14.095 pm 0.030$ mag (HATS-66). The Super-Neptune HATS-62b is the least massive planet discovered to date with a radius larger than Jupiter. Based largely on the Gaia DR2 distances and broad-band photometry, we identify three systems (HATS-62, -64, and -65) as having possible unresolved binary star companions. We discuss in detail our methods for incorporating the Gaia DR2 observations into our modeling of the system parameters, and into our blend analysis procedures.
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