"Incredibly, the loud-mouthed bragging, insulting youngster had been telling the truth all along."

Wrote the NYT, describing the fight that took place 50 years ago today:

Cassius Clay won the world heavyweight title tonight when a bleeding Sonny Liston, his left shoulder injured, was unable to answer the bell for the seventh round.

Immediately after he had been announced as the new heavyweight champion of the world, Clay yelled to the newsmen covering the fight: "Eat your words." Only three of 46 sports writers covering the fight had picked him to win....

The fight was Clay's from the start. The tall, swift youngster, his hands carelessly low, backed away from Liston's jabs, circled around Liston's dangerous left hook and opened a nasty gash under Liston's left eye....

But the kid hadn't lied. All those interminable refrains of "float like a butterfly, sting like a bee," had been more than foolish songs....

The youngster... the kid....

For weeks, Clay had played the fool and been tagged at will by unworthy sparring partners. This morning, at the weigh-in, he had acted bizarre and disturbed.

And tonight, he had been cool and fast and without fear....

Poetry and youth and joy had triumphed over the 8-1 odds. And until it had happened (and perhaps until they can look it up) people laughed at the thought that a night like this could happen.

The crowd had cheered lustily at 9:59 P.M., when Cassius came jogging down the aisle toward the ring, his face impassive, wearing a hip-length terry-cloth white robe on which was emblazoned, The Lip. Nobody even snickered, for everyone knew Clay to be a braggart, not to taken seriously....

Earlier, rumors had swept Convention Hall that Cassius was not going to show, that the thin line of hysteria he had trod during the morning weigh-in has become full-scale fear...

ADDED: Wikipedia has a good article "Muhammad Ali vs. Sonny Liston," about the 2 fights between these men. As for the first fight, the one that was 50 years ago today:

The brash Clay was equally disliked by reporters and his chances were widely dismissed. Lester Bromberg's forecast in the New York World-Telegram was typical, predicting that "It will last longer than the Patterson fight—almost the entire first round". The Los Angeles Times' Jim Murray observed, "The only thing at which Clay can beat Liston is reading the dictionary", adding that the face-off between the two unlikeable athletes would be "the most popular fight since Hitler and Stalin—180 million Americans rooting for a double knockout". The New York Times' regular boxing writer Joe Nichols declined to cover the fight, assuming that it would be a mismatch...

Liston trained minimally for the bout, convinced that he would dispose of Clay within the first two rounds. He typically ran just one mile a day, instead of his usual five, reportedly ate hot dogs and drank beer, and was rumored to have been furnished with prostitutes in training camp.

The television series I've Got a Secret did multiple segments about the title fight. Panelists Bill Cullen, Henry Morgan and Betsy Palmer predicted that Liston would win in the third, second, and first rounds, respectively. Host Garry Moore was even more pessimistic about Clay's chances, estimating a Liston knockout "in the very early moments of round one", adding, "if I were Cassius, I would catch a cab and leave town". Actor Hal March went a step further: "I think the fight will end in the dressing room. I think [Clay] is going to faint before he comes out." 

After the fight:

Sensing that he had made history, Clay quickly ran to the ropes amidst the commotion in the ring and shouted at sportswriters, "eat your words!" In a scene that has been rebroadcast countless times over the ensuing decades, Clay repeatedly yelled "I'm the greatest!" and "I shook up the world."

Clay had to be persuaded to hold the traditional post-fight press conference. He called the writers "hypocrites" and said, "look at me. Not a mark on me. I could never be an underdog. I am too great. Hail the champion!" The day after the fight, Clay announced that he was changing his name to Cassius X, but then he was given by Elijah Muhammad the name Muhammad Ali the following week.

It was the rematch where Ali knocked out Liston in the first round — watch it here — with a punch that many people thought was nonexistent:

Midway through the first round, Liston fell to the canvas, then seemingly struggled to his knees only to roll over on to his back. Few of the attendees saw Ali deliver a knockout punch. The fight quickly descended into chaos. Referee Jersey Joe Walcott, a former world heavyweight champion himself, appeared confused after Ali refused to retreat to a neutral corner. Ali initially stood over his fallen opponent, gesturing and yelling at him, "Get up and fight, sucker!"...

The blow that ended the match became known as "the phantom punch", so named because most people at ringside did not see it. Ali called it the "anchor punch" and claimed it was taught to him by the Hollywood actor Stepin Fetchit, who had learned it from Jack Johnson. However, Ali himself was unsure immediately after the fight as to whether or not the punch connected, as footage from the event shows Ali asking his entourage "Did I hit him?"