A possibly-complete list of languages of the world:

Language Spoken By
Aboleth aboleths, skums
Abyssal demons
Aquan water creatures, tritons, merfolk
Auran air creatures
Beholder beholders
Blink Dog blink dogs
Celestial celestials, Romus
Common most everybody, especially Gus and Shell
Dark Speech hardly anybody
Dinlun/Engineer engineers
Draconic dragons, kobolds, arcane spellcasters
Drow drow
Drow Sign Language drow
Druidic druids
Dwarven engineers
Elven elves
Feline catfolk, tibbits, cats
Formian formians
Giant giants
Gith githyanki, githzerai
Gnoll gnolls
Gnome engineers
Goblin goblinoids
Gol-Kaa goliaths
Grell grell
Grimlock grimlocks
Halfling halflings
Ignan fire creatures
Illumian illumians
Infernal devils
Kuo-Toan kuo-toa
Omorashi/Spirit Tongue the Omorashi Empire, Omorashi spirit creatures
Orc orcs
Plasper gropagas
Qualith illithids
Quor and Riedran kalashtar
Sahuagin sahuagin
Slaad slaads
Sphinx sphinxes
Sylvan fey, woodland creatures
Terran earth creatures
Thri-Kreen thri-kreen
Treant treants, trees
Tuilvilanuue raptorans, some birds
Undercommon most underground-dwelling races
Worg worgs
Yuan-Ti yuan-ti