Less sought-after is the reputation they acquired when they were expelled from the 1990 qualifying tournament for lying about the ages of their youth internationals.
The USA benefited most from their removal from their qualifying group, reaching the finals in Italy for the first time for 40 years.
So their record may be inglorious and few matches involving the team have lingered long in the memory.
But Mexico has played a key part in the tournament's evolution since its inception in 1930.
It was on a Sunday afternoon in mid-July of that year that Mexico took to the field for the first ever match in the tournament.
Admittedly they were thrashed 4-1 by France and only 1,000 fans gathered for the game.
But they were not helped by an injury to their goalkeeper Alex Thepot, who left the field after just 10 minutes to be replaced by the left-half.
There would be no substitutes allowed in World Cup matches for another 40 years.
With the French and Italians, the Mexicans are one of only three nations to have hosted the event more than once - in 1970 and 1986.
On both occasions they were unlikely hosts, selected ahead of Argentina in 1970 and holding the event 16 years later only when original hosts Colombia withdrew due to a lack of finance.
They made their first real impact in 1970, finally reaching the knockout stages at the seventh attempt.
But that achievement turned sour when the Italians defeated them 4-1 in a tournament dominated by Brazil.
If 1970 belonged to Brazil - and Pele in particular - 1986 belonged to Maradona.