There appears  to be some question regarding car rental and driving in Mexico and, having lived in Latin America for a number of years, here are some experienced based suggestions on the subject. 

In most countries in Latin America, Mexico included, traffic signals are mere suggestions, so approach each intersection with caution.  Turn signals may indicate a driver is actually turning, but maybe not.  And, the driver may be turning with no signal at all.... use caution and expect anything!

                                     Approach Intersections With Caution

It is quite common to approach an intersection with cars from 4 directions, jugglers between the lines of traffic and skateboarders flying down the middle of the street.  Add to this a few buses, some loose dogs, honking cars, a traffic signal that may or may not be working, and you begin to get the picture!  

Foot traffic in the form of adults, children, dogs, bicycles and skateboards abound and while pedestrians do not legally have the right of way, as a foreigner you most certainly do not want to hit anyone!  It is best to limit your driivng to daylight hours both from a personal safety issue as well as accident prevention.  Many cars travel at night without lights, including trucks and police cars!  

                                            Follow Standard Safety Rules

Standard safety rules, lock your car, don't leave valuables in the car, and don't leave your passport anywhere certainly apply.  If you are going to be in Latin America for an extended time, it might be advisable to have a notarized copy of your passport made instead of carrying your official copy.  A local Abogado, lawyer, can provide the necessary signatures or stamps that are required to make your color copies official.  Locking your true offical passport in the hotel safe is a good idea.  Many times, if you are stopped the police will want to see your passport, not your driver's license.

Make sure you purchase generous insurance coverage when renting a car, this is not the place to cut corners.  If you need to tighten your budget do it somewhere other than car insurance.  If you have adequate insurance coverage you can relax and enjoy the experience of driving in Mexico. 

Try to learn at least the basics of Spanish, it really helps.  Don' t believe what you read about  'most', 'a lot', 'many' people speaking English.  While it may be somewhat true, not everyone that knows a little English is willing to admit it and speak.  They would rather let you struggle with Spanish than embarrass themselves with English.  People in all the Latin American countries very much appreciate your efforts to speak their language and will be most helpful.

                                               What To See In Mexico

While having a car at your disposal really opens up the opportunities to see the 'real' Mexico, it is also wise to schedule some guide assisted tours in the areas you will be traveling to.  This will greatly enhance your overall vacation experience.

Below are a few ideas of what Mexico has to offer:

Teotihuacan Pyramids and Shrine of Guadalupe

 Teotihuacan Pyramids and Hot-Air Balloon Tour

4 in 1 Tulum Adventure:  Zipline, Cavern Rappel, Cave Snorkel and Skycycle

Sian Ka'an Multisport Eco Adventure

Captain Hook Cruise in Cancun

Cancun Dolphin Swim Adventure

Tulum and Xel-Ha from Riviera Maya

Mexico City Sightseeing Tour

 Puerto Vallarta Sunset Cruise and Candlelight Dinner Show

 Marietas Islands: Cavern Swim and Snorkel Cruise From Puerto Vallarta

When renting a car you can use a global booking agent, helpful if you do not speak Spanish, and typically all inclusive, or a local agent.  Below are a few sites to get you started.

Renta de Autos - car rental throughout Mexico.  Compares prices from over 500 car rental companies - Site in multiple languages including English

Renta de Autos DF - Car rental Mexico City - Site in Spanish and English

Renta de Autos Guadalajara - Car rental in Guadalajara - Site in Spanish and English