There are games that go to great lengths to create elaborate and internally consistent languages to add a greater degree of depth and ambiance to the world in which they are set.
Starcraft is an example - the Protoss address the player with phrases like "En Taro Adun, Executor", which, while not as fleshed out as the speech of the Talan does make for a fictional language .
Outcast, the game featuring the aforementioned Talan even comes with a basic dictionary in the manual helping you to work out what the locals and your enemies are saying when they're not speaking English, "Zort" being among the more easily understood phrases.
Richard Garriott discusses the construction of his Tabula Rasa script in a talk with Warren Spector (around 02:28) at the University of Texas.
In Fumito Ueda's debut game, characters Ico and Yorda speak in imaginary languages, unable to understand each other. Ueda has been quoted as saying the boy's language is similar to Chinese while the sound of Yorda's words is inspired by French, though others have described them as "backwards Japanese/Latin". The language in ICO prequel Shadow of the Colossus is said to be more heavily influenced by Latin "to make it sound more ancient"...
In the PAL version of ICO, when first played, Ico's speech is subtitled in English while Yorda's is transcribed in a strange script reminiscent of hieroglyphs. On a second playthrough she too is translated into English. This feature is missing from the NTSC release .
Panzer Dragoon is also well known for its language, Panzerese. Created by Yukio Futatsugi as somewhat of a hobby, it is a mixture of languages like Greek, Latin, and Russian. Panzerese is also used in the spoken parts of Breath of Fire: Dragon Quarter.
Ueda has said he used language in this way to create an air of mystery.
"Personally, I often import games from abroad and play them. On such occasions, my imagination is sometimes stimulated more as I don't understand the language. ICO is a game which intentionally tries to achieve this effect."
Some games choose to use a form of random gibberish in lieu of voice acting, intonation being the only information beyond the text or icon it underlines. It serves more to alleviate the dryness of text /symbols alone than to communicate. For more information on this, view the gibberish concept page.
Some games, like Final Fantasy X, Star Fox Adventures, and Fez simply use written English filtered through some type of cipher.