Abyssal is the language of demons
Celestial is primarly spoken by celestials and priests.
The world's Lingua Franca, simply known as "common"
Deep speech is typically spoken by abberations
The ancient language of Dragons and Dragonborn
The main language in the Dwarven Empire, and mother tounge of most of the world's dwarves
Elvish or elven was the official language of the Alyssian Empire and is still widespread across the Alyssian continent to this day
Spoken primarliy by giants and creatures living high up in the mountains, including firbolgs and trolls
Gnomish is spoken primarliy by gnomes
Sometime during the Black Age goblins appear to have decided they, too needed their own language, and to this end they started talking what is commonly reffered to as "common but weird"
Halfling is spoken primarly by Halflings and those who trade with them
Infernal is the language of devils
Orc or Orcish is a language spoken primarly by Orcs
Primordial is the language of primordials and elementals
Sylvan is the language of fey
Undercommon is the most common language of the Underdark