I feel it depends on the game.
Games like Mass Effect, Uncharted, and Assassins Creed really require it for the game to feel right and flesh out the character you play. However, games like Fallout and Half-life function BETTER when you play a character without a voice to hear.
Contrary to what people may think, I feel some games need the old book method of "imagine the voice in your head". Not to mention the fact that not every character needs to speak to be great. Actions speak louder than words, and no one exemplifies it more than Gordon Freeman.
Then again, Commander Shepard saved humanity, but seems to to be able to get a word in quite nicely.
There's room in games for both.