When they're not redundant.
If you have the knife-wielding maniac springing out of the closet—or bursting, or lunging—the verb has an understood "suddenly" in it. If you write that the maniac suddenly burst out of the closet, you have, in effect, an extra "suddenly," which has nothing to do but shuffle its feet and look sheepish. Very suddenly, of course, is right out. It adds another useless word. You don't want words that aren't pulling their weight.
Dialogue, as others have noted, is different. So is first person narration, or anything else where you need to catch the rhythm of a character's speech. And, y'know, you might come across a description that works better with "very" in it. These words aren't inherently bad. It's just (there's one!) that they're often pointless.
Izunya