Silent protagonists have worked very well for years in series such as Zelda, Dragon Quest and Pokemon. They are a staple of those series which not only work well, but show how you can make a game focused on one and make the players experience come out stronger for it.
Other games and series have had case by case experiences with the idea. A series like Chrono did it well, though both Protagonists didn't really need to stay silent and mostly did so due to the imput of the creators (Yuji Horii). While others, say your main character in Knights of the Old Republic, did so as a response to multiple questions and commands, and not so much because he was mute (he actually has a couple words of spoken dialogue in battle).
On the whole however, the view really is that the silent protagonist can enhance the experience and options of the player...but only if implemented properly.
Six upcoming games you should look into:
