Tough question, since cinema was widely used as a propaganda tool and the country has changed so much in the last century.
Redes (1936), an Eisensteiniasque film about fishermen in Pátzcuaro, beautiful propaganda.
Danzón (1991), a nice story about a telephone operator going to Veracruz, searching for her lost dancing partner and finding new friends, and a lover.
Reed, México Insurgente (1973), the Revolution de-mitified.
Arráncame la vida (2008), life, love and politics in the 1940s through the eyes of a woman.
El Compadre Mendoza (1934), first study on political opportunism during the Revolution
La sombra del caudillo (1960), a classic about political treason in the 1920's, the film was prohibited from 1960 to the mid-1980's.
María Candelaria (1944), another beautiful classic, idealizing indian life and its supposed incompatibility with modern values.
La Ley de Herodes (2000), an acidly funny story of an idealistic politician turned into a big corrupt "winner".
Los Caifanes (1966), urban social class cultural differences clash in a wild night out.
A toda máquina (1951), I would be damned if I didn't include in this list a film with Pedro Infante, the biggest national and nationalistic film icon. This is a comedy about male friendship -half way between hard competition and a man-crush- between two traffic police agents.
That's my list.
But the first film that actually came to my mind is
Nosotros los Pobres (1949), "We, the Poor".
Everyone agrees now that it's a terribly manipulative and sentimental film (it became a trilogy), but it has been certainly the most popular one in the history of Mexican cinema (inside Mexico, that is).
Everything goes wrong in poor Pedro's life, a carpenter in a working class neighborhood in Mexico City, any conceivable tragedy falls upon him, and he keeps on working and fighting and hoping, only to have his hopes crushed by yet another tragedy.
Millions of Mexicans know by heart several lines of the film, but they're used now to make jokes.