"I believe the road to hell is paved with adverbs, and I will shout it from the rooftops." Stephen King, On Writing.
The above is one of the most quoted "rules" Stephen King identified in his book on the craft, On Writing. From my experience in writers' forums, it also seems to be the most misunderstood. Nary as month goes by without someone typing "... but I checked [insert random famous title here] and they use many adverbs!" In most cases, I suspect the problem is those asking haven't read Mr King's book, and many desire to take such rules as literal absolutes. The complaint is so frequent I decided to write a blog post on it, rather than keep typing the same answers ad nauseam.
Remember: this is my opinion and interpretation. If you see it differently, I'd be happy to chat about it in the comments or on my FB page.
So, let's start at the end, by examining what this quote doesn't say: It doesn't say you can't use adverbs. Go back to check and you'll agree. Yes, it casts them in a negative light — for good reason — but it doesn't prohibit their usage.
If you read the book (and I recommend you do), the deeper meaning of this statement becomes clear. Adverbs have their place, but often there's a more powerful phrase available. To borrow Mr. King's analogy; each writer carriers a literary toolbox in their mind, filled with words, grammar, and techniques. Adverbs are a tool in that box, but they are a blunt instrument. Often, there is a more appropriate option.
Let's unpack the previous paragraph. What do we mean when we talk about a sentence being more powerful? Every sentence communicates a message. The more words we use to craft it, the weaker that message becomes. It's like watering down alcohol; you're drinking the same thing, but it has less flavour, and packs less punch. Adverbs, by definition, add to an existing verb in a sentence — they dilute your writing.
What's the alternative? Find a more appropriate verb.
The simplest example I often use is a character running down the street. Consider the two sentences:
1. "Jane ran quickly down the street."
2. "Jane sprinted down the street."
The first sentence uses a generic verb (ran) and an adverb to tell us Jane was really running down the street, not jogging comfortably. The second tells us the same thing, but with one less word. It commincates the scene more efficiently, and using more specific verbs results in less repetition.
Note: Someone correctly pointed out that sprinting and "running quickly" are not always the same thing. When you use a specific verb, you are applying a specific meaning. As such, this only works when there is a specific verb that accurately illustrates the scene you are creating.
Whenever you use an adverb, ask yourself whether there's a more appropriate verb you can use instead? Sometimes there won't be a better option. That's okay — when this is the case use the adverb. Also, remember people use adverbs a lot when talking, so don't feel you need to eliminate them all from character dialogue.