Don't you hate it when somebody says something that's nice on the surface, but actually laced with venom? The passive aggressive voice over is perfect for when your reads require just the right amount of anger bubbling under the surface.
Some people have perfected the art of damning with faint praise, or conveying a tone of barely-hidden irony that seems like the "right" thing to say, but in reality has an undercurrent of hostility. The passive agressive voice is the perfect vocal Trojan horse for those characters that don't have to scream to verbally attack someone else. Their approach is all about sliding their bitterness under the table and creating a situation of plausible deniability. Some are more overt, and some are covert, but one thing's for sure: they don't mean well.
Film, literature, animation, and video games have a veritable who's who of passive agressive voice showcases. Whether it be the sassy, intellectual party member in an RPG who never seems to know when to keep the wry remarks to themselves, or the smart-alecky protagonist that could use a better bedside manner, there's a whole spectrum of characters to explore. In ads there's always that sarcastic character with a mean streak right under the surface, and is usually a great counterpoint to more straight-laced characters (but hey, remember not to make the ad itself passive aggressive!).
Sarcastic, dishonest, and with barely-concealed content under the hood. The passive agressive voice does not mean what it's saying, even when the words out of the character's mouth read like straight compliments.