Everyone will remember the antics of Diego Maradona during the 1986 World Cup encounter between the two nations, while events 12 years later in Saint Etienne will forever be imprinted on the mind of David Beckham.
It is a rivalry that was born 64 years ago today as the Argentines became only the second international side after Scotland to face England at Wembley.
The South American nation had been invited to play as part of the Festival of Britain, but they threatened to ruin the celebrations when against the run of play, Mario Boye broke the deadlock in the 18th minute.
Angel Labruna beat England goalkeeper Bert Williams to a loose ball and with a narrowing angle he decided instead to cross towards the back post, where Boye was waiting to power a header into an unguarded net.
What followed was one of the most memorable goalkeeping performances at the famous old ground, as Argentina's Miguel Rugilo made a string of impressive stops to thwart the home side.
However, his good fortune ran out 11 minutes from time when England drew level. Tom Finney's corner was flicked on by Harold Hassall for Blackpool centre-forward Stan Mortensen, who evaded his marker to squeeze his effort inside Rugilo's near post.
Then, four minutes from the end, England's pressure told once again. Alf Ramsey's lofted cross was knocked down into space by Mortensen and it was Jackie Milburn that reacted quickest to fire in from close range.
The hero of the encounter, though, was Rugilo, who had his stubborn performance recognised by supporters at the final whistle with a standing ovation.
From England's point of view, the win meant that they had still not lost to a foreign side at Wembley.
England: Williams; Ramsey, Wright, Taylor, Eckersley; Cockburn, Finney; Mortensen, Milburn, Hassall, Metcalfe
Argentina: Rugilo; Colman (Allegri), Faina, Pescia, Filgueiras; Yacono, Boye, Bravo; Labruna, Loustau, Menendez