I've never been prone to picking "favorite authors." If I like something, I like it; if I don't, I don't. I decide how I like things on a case by case basis. It takes a lot of consistently good work from someone for me to proclaim that I like "their work."
I mention this merely because I've never really liked Arthur C. Clarke. Sure, he's a giant of science fiction and all that, but his work is generally too cerebral and a bit too arrogant for my own personal tastes. (There's a discussion penned by Clarke on how an alien might look here. It operates under some odd assumptions, the primary one being that intelligent aliens would naturally be more efficient than ourselves. It also insisted that the human hand was good enough that it was okay to anthropomorphize it when designing aliens. That's an odd set of assumptions to play against each other.) If you disagree, that's fine-you get to decide what your tastes are. But Clarke's works aren't quite to mine.
A Meeting with Medusa, however, is a Clarke story that plays to his strengths, and is definitely my favorite such.
Why? If nothing else, it's a first contact story that created the entire modern concept of what life on a gas giant would be like. If nothing else, that would be enough to secure it a place in my own personal literary canon.
What really makes it work is that it's a simple voyage of discovery. It's not about bizarre, high-falutin' concepts like ascension to godhood and contact with things we can't understand. In this story, a man goes into space, goes to Jupiter, and then meets some aliens. How smart they are or aren't isn't much gone into, but that's not important-it's just first contact, after all. (And it's hard to hold a conversation with a mile-long sky jelly that's possibly trying to eat you.)
There's an element of transhumanism in the story; that is to say, in a surprise reveal at the end (sorry for the spoilers), we learn that the pilot was a cyborg who was so extensively modified he moved around on wheels. It was his opinion that mankind couldn't own the stars, and that only fully sapient mechanical intelligences could manage to survive and prosper in deep space. (His argument is probably sound, all things considered.) It's a bit of a downer, really, but that's probably the other reason I'm not a huge fan of Clarke's. (Give me Asimov any day.)
A strong story all around, and one I'd recommend reading if you can find it.
On a side note: The cover on Wikipedia is for the same version I own. Ironically, the printing I have, at least, has a printing error that attributes authorship to Kim Stanley Robinson (whose book Green Mars was co-printed as a "double" book with it).