Yes, I confess to my own part in the misconception that good writing is full of them. I did once *gasp* encourage students to slather their poetry with adjectives and adverbs, but I do have a defense: You know how you've read that Picasso had to be able to paint realistic scenes in order to hone the skills that allowed him to create his own masterful style? Well, while beginning writers are learning to choose the exact right noun or verb, adjectives and adverbs help create the images that bring life to the page.
Stephen King says in On Writing (y'all know how I love that book): "I believe the road to hell is paved with adverbs, and I will shout it from the rooftops. . . they're like dandelions. If you have one on our lawn, it looks pretty and unique. If you fail to root it out, however, you find five the next day . . . fifty the day after that . . ."
It's no accident that Hollywood uses the term "wrylies" (as in "he said wryly") to criticize overuse of parentheticals in screenplays. If you're doing your job with dialogue, your readers will know the tone of the lines without adverbs or parentheticals to guide them.
"But I like adverbs!" she shouted defiantly. (Bad.)
"Fine," he said. "You may continue to show your ignorance on hundreds of pages of adverb-filled prose." (Good.)
One of the best tips I ever heard was from a woman at a B'ham SCBWI meeting who told me, when we were discussing adverbs at a cocktail dessert party (ah, the social skills of writers) to run an "ly" search on my manuscript after I thought I'd rid my novel of adverbs. I was shocked at how many were still there! Did I delete all of them? Of course not! But I made freakin' sure they were all really, totally, completely, undeniably, indisputably needed. (Yes, those adverbs were intentional. I was just havin' a little fun.) Thank you, nice blonde-haired lady. I wish I knew your name to give you credit. If you're reading this . . .
*Note: Two years after I wrote this (and five years after it happened,) I actually recognized the nice blonde-haired lady at another SCBWI conference and told her how helpful her adverb tip had been. So now I can appropriately thank Cathi O'Tyson for her great advice and for being a new writer friend; we can't have too many of those!