Here is the list of the different languages that are commonly available. I'm not going to list EVERY language as that would take quite some time. I'm focusing on the more common languages and their variations. If there is something you want to learn that you don't see here, let me know. Most likely it will be available.
Trade Common (or just Common) - this is the default if you don't take any spoken languages. Used by most civilized races to conduct business. Has a written form.
Akorian - this is the language of magic as most non-elven spellbooks were written in Akorian, and the practice continues to this day. It is a spoken language as well, although a bit tougher to carry on conversations about many mundane things. Still many of the ruling class of the Kingdom of Immater chose to speak this over Common or Barivish. Taking at least reading/writing is mandatory for Mages.
Elvish - this is the basic elven tongue used by all sub-races. A few differences in speech patterns or phrase usage may occur but can be understood. Has a written form.
High Elvish - this is the language of the elven ruling body, spoken by grey, and now high, elves to conduct important business. It is also what elven spell books are written in. Taking at least reading/writing is mandatory for elven Mages.
Draconian - this was the language of the dragons but is now a dead language. Still there are a number of ancient texts and writings one may stumble upon so learning the written form might be valuable for treasure seekers and historians. It can be taught by only a few cultures so learning it could be an adventure all its own. No one may start the game knowing this. No longer a spoken language.
Barivish - this is a common language spoken by people all along the southern part of the continent, not just in Barivain. It's an easily grasped language for many and provides another means to communicate besides Common. Many gnomes, half-elves and some dwarves learn this language as well if they spend much time in any of the southern kingdoms. Has a written form.
Rhidhen - this is the language of the northern kingdom. It differs greatly from the southern kingdoms and trade common. It has a written form that incorporates runes for many of its words and simple phrases. Only characters from Rhidhelmark may start with this language known.
Dwarvish, Gnomish, Orcish, Goblin - these are all the racial languages of the larger populations of demi-humans. They all have written forms that can be learned. Like Elvish, there my be differences in speech patterns and phrase usage between the different sub-races but it can still be widely understood.