With the heads up I poked around and according to the MM the following languages exist.
Abyssal, Aquan, Auran, Blink Dog, Bullywug, Celestial, Common, Deep Speech, Draconic, Druid, Dwarvish, Elvish, Giant, Giant Eagle, Giant Elk, Giant Owl, Gith, Gnoll, Gnomish, Goblin, Grell, Hook Horror, Ignan, Infernal, Modron, Orc, Otyugh, Primordial, Sahuagin, Slaad, Sphinx, Sylvan, Terran, Thieves, Thri-kreen, Troglodyte, Umber Hulk, Undercommon, Winter Wolf, Worg, and Yeti. And the PHB has Halfling bringing the count up to 42.
Two special notes, Primordial allows you to speak Auran, Aquan, Ignan, and Terran (and apparently primordial?). The secret languages "Thieves Cant" & Druid can both be learned with DM permission.