He's best known for many performances and recordings alongside Maria Callas; they were both under contract to EMI in the '50s and he was the tenor lead on most of her complete opera recordings. (They also had a brief, unhappy reunion tour in the '70s; the recital recording they made at that time was so bad that it was never released.)
He was a bit similar to Luciano Pavarotti (whom he outlived) and Jose Carreras in that he had what was basically an exceptionally beautiful lyric tenor voice but pushed it too hard in big, heavy roles. But while Pavarotti continued to sing well for many years, Di Stefano combined his over-heavy roles with a lack of discipline -- record producer John Culshaw recalled that his party-hard lifestyle seemed to mean more to him than singing -- and so he'd all but ruined his beautiful voice by the early '60s. You can hear this very clearly if you compare two excellent recordings of Puccini's Tosca. Di Stefano sounds great on the famous 1953 recording with Callas; in 1962 he recorded the opera again in Vienna with Leontyne Price and Herbert Von Karajan conducting, and he sounds very strained.
Here is what Culshaw wrote about his first encounter with Di Stefano in his (not always reliable) autobiography, "Putting the Record Straight":
At the mere mention of his name, stage and recording producers had been known to turn white and run as fast as possible in the opposite direction. He had little respect for most of his fellow artists and hardly any at all for conductors. Rehearsals bored him. Above all, he liked the elegant pastimes of life (such as fine food and fast cars), and he was a compulsive gambler with a very unreliable track-record. Yet I took to him at once. Although he was still a relatively young man, his voice was already beginning to show signs of the wear and tear imposed by the life he lived; but he was in all other respects intelligent, and as a musician he was a natural. The eventual, almost total breakdown of his voice some ten years later was attributable to a life-style he could not abandon because it meant more to him than singing. Even at his worst, almost everyone forgave him everything, partly because of his intelligence, partly because of his Sicilian good looks, but mostly because of his charm. It is apt to use the cliche that he could charm the birds out of the trees, except one would have to add that Pippo -- as just about everyone called him -- would then doubtless proceed to eat them alive.
Here he is sometime in the '50s (not sure what year) in Rigoletto:
Here's an audio clip of him in 1950 (in his prime, in other words) singing Madame Butterfly with Renata Tebaldi in a broadcast recording from San Francisco.