In Tevinter we speak Tevene and the Trade tongue...well Teven is spoken mostly by the nobility class as the Trade tongue has become the common language that most everyone on Thedas speaks regardless of their secondary language.

Orlesians speak Orlesian and Trade, Antivans speak Antivan and Trade, Elves speak Elvish...rather the Dalish speak Elvish, the Qunari speak Qunlat, the Dwarves well they invented the Trade language more or less, in the Anderfels they speak Ander, in Rivain they speak Rivaini.

There is very little cross communication between the languages though...I suppose Orlesian and Antivan sound similar at times.