Most writing geeks are not fans of adverbs, and I'm no exception. If you believe you're a good writer who has mastered the basics (maybe you've received good comments from your teachers, professors, or peers), consider eliminating as many adverbs as you can from your writing and replacing them with good, strong verbs.
An example: She walked slowly into the classroom.
That's correct usage, but this is a post about writing, not grammar. And from a writing standpoint, that sentence is boring and not very informative. Is she walking slowly because she's, well, a slow walker? Or is she sad? Infirm? Afraid? A strong verb can give the reader a lot more information about what's going on.
She trudged into the classroom. (Here, I think she's sad; maybe she's bummed that she forgot her homework.)
She drifted into the classroom. (I think she's daydreaming about something. Maybe her boyfriend is out in the hall.)
She staggered into the classroom. (Wow...maybe someone stabbed her and the knife's still in her back?)
Adverbs still have their place. They can help put the finishing touches on an already strong sentence (She trudged into the classroom, silently cursing to herself). But adverbs are overused by a lot of writers. If you can learn to substitute strong verbs whenever possible, you're taking your already-good writing to the next level!