1. Nahuatl: Spoken by the Aztecs, Nahuatl was the most widespread language in central and southern regions of Mexico.
2. Mayan Languages: Several Mayan languages were spoken by the Maya people in the Yucatán Peninsula and adjacent areas. These languages include Yucatec Maya, Quiché, Tzotzil, and Tzetzal, among others.
3. Otomanguean Languages: This language family includes several languages spoken in central and southern Mexico. Some of the notable Otomanguean languages are Otomi, Mixtec, Zapotec, and Mazatec.
4. Tarascan: Spoken by the Purépecha people, the Tarascan language was primarily spoken in the present-day state of Michoacán.
5. Totonac: Used by the Totonac people in the central and eastern parts of Mexico, especially in the state of Veracruz.
6. Huastec: Spoken in the north-central region of Mexico, Huastec belongs to the Mayan language family.
7. Tlahuica: Primarily spoken in the state of Morelos in central Mexico.
It's important to note that there were numerous other indigenous languages spoken in Mexico before the Spanish invasion. These languages represent the cultural diversity that existed among different pre-Columbian civilizations and ethnic groups in the region.