In 1970 Brazil's third victory entitled them to claim the Jules Rimet Trophy permanently, and a new trophy, the World Cup Trophy, was contested at the next tournament, four years later in West Germany.
The World Cup Trophy will not be retired until the name plaque has been filled with the names of the winners, and is expected to remain in use until 2038.
As well as winning the original trophy three times, Brazil have won the World Cup Trophy twice.
Italy won the original Cup twice and the new Trophy once, in 1982.
Germany/West Germany have won the tournament three times, twice lifting the current Trophy, and Argentina have also won the current Trophy twice.
But even if they win it again, no-one will receive this Trophy outright.
This year's winner, Italy, received only a replica of the World Cup Trophy regardless of how many times they have won it.
The Jules Rimet Cup
Two years before the inaugural FIFA World Cup in 1930, the newly drafted regulations stipulated that the winners should be rewarded with a new trophy, with French sculptor Abel Lafleur being assigned this prestigious task.
The little trophy had a somewhat hazardous existence. The Italian Vice-President of FIFA, Dr.Ottorino Barassi, hid it in a shoe-box under his bed throughout the Second World War and thus saved it from falling into the hands of occupying troops.
Then in 1966, the cup disappeared while on display as part of the build-up to the World Cup in England and was only recovered, buried under a tree, by a little dog called Pickles.
Finally, in 1983, it was stolen again, this time in Rio de Janeiro, and apparently melted down by the thieves. The Brazilian Football Association, who had earned the right to keep the trophy after having won it three times, ordered a replica to be made.
The original trophy was 35cm high and weighed approximately 3.8 kg. The statuette was made of sterling silver and gold plated, with a blue base made of semi-precious stone (lapis lazuli).
There was a gold plate on each of the four sides of the base, on which were engraved the name of the trophy as well as the names of the nine winners between 1930 and 1970.
The Current FIFA World Cup Trophy
With the Jules Rimet Cup now in the permanent possession of Brazil after their third World Cup triumph in Mexico City in 1970, FIFA commissioned a new trophy for the tenth World Cup in 1974. A total of 53 designs were submitted to FIFA by experts from seven countries, with the final choice being the work of Italian artist Silvio Gazzaniga.
He described his creation thus: "The lines spring out from the base, rising in spirals, stretching out to receive the world. From the remarkable dynamic tensions of the compact body of the sculpture rise the figures of two athletes at the stirring moment of victory".
The current FIFA World Cup Trophy cannot be won outright, as the regulations state that it shall remain FIFA's own possession. The World Cup winners retain it until the next tournament and are awarded a replica, gold-plated rather than solid gold.
The new trophy is 36 cm high, made of solid 18-carat gold and weighs 6175 grammes. The base contains two layers of semi-precious malachite while the bottom side of the Trophy bears the engraved year and name of each FIFA World Cup winner since 1974.