Aeromexico
Aeromexico is Mexico's largest airline, and is based in Mexico City. It offers a huge selection of international destinations in the U.S., Europe, Central and South America and Asia---as of October 2009. It is the only Mexican airline that flies direct to Asia. It has a regional subdivision called Aeromexico Connect that covers 38 destinations in Mexico and seven in the U.S.
Mexicana
Mexicana is Mexico's second-largest airline. It operates both regionally and internationally as one company, with flights within Mexico and to the U.S., the Caribbean, Central and South America, and Canada.
Aviacsa
Aviacsa is a mostly regional, budget airline. Their one destination outside Mexico is Las Vegas, interestingly---no California. Their English website is sometimes down, but fortunately their flights appear on flight aggregator websites such as Kayak and Travelocity, where the flights of other Mexican regional airlines do not.
Viva Aerobus
Based in Toluca, Viva Aerobus is a budget airline created as a joint venture of Mexico's biggest bus line, IAMSA and Irelandia, the investment vehicle of the family that owns Ryanair. Their planes are all Boeing 737s, and they fly both regionally and internationally.
Interjet is a regional-only line that also operates from Toluca, with a fleet of Airbus A320s. Their website is Spanish-only, but don't let that deter you---it's set up like most English sites, and isn't too difficult to figure out with some effort. If your Spanish just isn't up to snuff, though, you can always book through a travel agent.
Volaris
Volaris is another airline operating a fleet of Airbus A320s, which on average are only 2 years old---the company prides itself on having Mexico's youngest fleet. Volaris is mostly regional, but they have two non-Mexican destination: San Francisco/Oakland (SFO) and Los Angeles (LAX).