Depends on the game. Worked really well in Half Life 2, where everyone was telling Gordon to go do X thing a certain way and then when he'd accomplish said task they'll praise him and he just stares. It was almost satirical, added a bit of dark humor. Another somewhat silent protagonist that works is Link, even with dialogue options in the new Skyward Sword he still lacks a voice. Since I started playing Zelda games Link has a certain kind of voice in my head that I wouldn't want to be replaced by an actor/actress. Skyrim is another great example since it adds to the whole role playing as whoever you want element.
On the flip side, having a voiced character allows a deeper story to be told relating to the protagonist. An example would be Resident Evil 4 where Leon's past was revealed through dialogue. Another game with a solid voiced character was Deus Ex: Human Revoultion. He had a grizzly "I'm the Batman" voice which added to his persona of being a bad ass.
On the flip side, having a voiced character allows a deeper story to be told relating to the protagonist. An example would be Resident Evil 4 where Leon's past was revealed through dialogue. Another game with a solid voiced character was Deus Ex: Human Revoultion. He had a grizzly "I'm the Batman" voice which added to his persona of being a bad ass.