IMHO, many of the great bits of dialogue in literature are not natural. Try recording an informal conversation and playing it back. What you get is a jumble of sentences, interruptions, and repititions. If you try to reproduce actual dialogue, it will fall flat.
What you should do is produce dialogue that seems natural, but actually is "filtered". Reading aloud is a good method. If it sounds good, bung it in!
Bingo!
Back when I was studying to be a psychologist, we had to record our sessions with clients, then type them out. In Cognitive Behavioral Psychology, sessions are structured and orderly. With just me and the client in this structured environment, man was I shocked when I started typing up our conversations! I would ask a simple question and often get rambling answers that contained questions, rabbit trails, and way more words than were necessary to answer the question.
As Nandu pointed out, we must write dialogue that sounds natural but that is NOT natural--or the reader's head will spin and he'll end up throwing our book out the nearest window.
I'm a-thinkin' that if you find your dialogue feels wooden, it might be that you need to intersperse it with a little "showing." Observe:
"You stink," said Fred.
"I know I do," said Betty.
"You stink!" said Fred, turning away and waving a hand before his nose.
"I know I do, and I quite like it," said Betty, poking her nose into her armpit and inhaling deeply. "Ahhhhh!"
Especially with longer bits of dialogue, try bringing the reader into the head and body of the speaker or listener ("...as Larry carried on with his monologue, Letitia made her way to the open window. Grandma's beans and onions had kicked in and, wanting to maintain Larry's respect, she had no desire to fumigate him..."); let Reader see how the environment acts on the characters (Marty's giving the graduation speech at high school... "...and, as our Waldo Meade High's founder, Waldo Meade, once said..." A snicker followed by a loud cough floated up from the audience; Marty's classmates were anxious to get to Disneyland, but he had a message to give them and, doggone it, he'd give it to 'em!); and so on.