For an example, I really liked how in Binary Domain, the writing was serious but still kinda campy, and the voice acting reflected that. Characters like Faye or Big Bo wouldn't've been nearly as compelling or funny if they didn't have voices and only had words on the screen.
On the silly or campy things working in the game's favor, I don't mind that kind of thing in an action game like Star Fox or Mega Man. The really silly dialogue and voice acting in Mega Man X: Maverick Hunter (the PSP remake of the first X), that game was made 100% more hilarious by the voice acting. Someone trying to be serious while confronting his friend Launch Octopus was absolutely fantastic
At the same time on the bad side of things, also from Binary Domain, the main character is not only his own character, but also the player's avatar, and considering that they intend you to voice him yourself for most of his decisions, that reaallly broke my immersion in the early stages especially.
Ultimately I say games like the Witcher or Saints Row 3 and 4 have it down. The charcter you play is effectively your avatar in what you decide they do, but their voice acting, especially in the story arcs, really makes them their own memorable character.