US PHONES THAT WORK IN MEXICO:
Depending on your plan, phones with the following US carriers can work in Mexico:
AT&T has extensive coverage throughout Mexico, most of it on their own newly upgraded 4G network. They now offer "AT&T Mexico Roaming Bonus" to Mobile Share Value consumer and business customers for free which allows unlimited texting to anywhere in the world and unlimited voice calling within Mexico and from Mexico to the United States. Additionally, customers will get 1 GB of data to use while in Mexico (with overage charges of $20 per GB).
Cricket is a prepaid service owned by AT&T. Cricket phones will work in Mexico for Talk, Text and Data at no additional charge with the $50 and $60 plans and currently uses a mix of AT&T and non-AT&T networks.
GoSmart is a prepaid from America Movil that offers the unique capability of roaming in Mexico and every other Latin American country. That's 15 countries from Mexico southward. GoSmart offers some very low price points and gives you unlimited data and will "throttle" your web speed after your high speed allotment. They have a limited number of phones available, but they allow you to bring your own phone. Broadband access is limited to 3G downloads but allow 4G-LTE access to Facebook and Messenger in the US and Latin America.
METRO BY T-MOBILE
Metro by T-Mobile is a prepaid service that roams in Mexico with an add-on that gives you the same Voice, Text, and Data allowance while Roaming in Mexico as you have in the US. Limited to plans $40 and over. Depending on when you add the feature, the "Mexico Unlimited" plan is either Free or $5/month. Yes, Metro roams on the same networks as T-Mobile.
With a Sprint phone you can roam in Mexico and several other countries across the Americas with no additional charges for Voice, Text and Data. You will need a Sprint "International" phone and plan, and there are a few limits such as roaming percentages and a 1Gb Data limit. If your phone worked in Mexico before the T-Mobile/Sprint merger, it will work as good as, or better, after.
T-Mobile phones work well in Mexico and reports are they use multiple networks. T-Mobile's regular plans allow you to roam in Mexico with either reasonable, or no, additional fees. Their "Mobile without Borders" plan allows you to roam in Mexico (and Canada) with no additional charges for Voice, Text or Data. This includes calls TO & FROM the US, Mexico and Canada with Data included, with download speeds up to 4G LTE rates, if you can find it. T-Mobile Pay-As-You-Go phones will also roam in Mexico but the per-minute rate is very high. T-Mobile's "Wi-Fi Calling" app allows voice calls made through wi-fi at no additional charge but in light of their broad roaming capabilities, Wi-Fi calling is a better option for where you have no cellular signal but do have Wi-Fi.
US Cellular phones with postpaid plans can roam in Mexico, although your roaming ability is phone model-dependant. Rates include a $3 per day surcharge, plus $.99 per minute, plus any pass-through toll charges from the foreign carrier. Text and Data roaming are not currently available.
Older Verizon phones have limited roaming capabilities, but if your Verizon phone finds a signal, it will work. Newer Verizon phones will roam on one of the GSM networks. They offer Mexico plans which allow roaming in Mexico for about $15 more than regular plans. Data roaming charges are $.005/KB ($5.12/MB). Plans without free Mexico Roaming, incur a charge of .99 per minute for both incoming and outgoing calls within Mexico. Text Messaging in Mexico is .50 Sent, .20 Received. Both postpaid and prepaid Verizon phones work in Mexico at the same per-use rates. Verizon offers a Global Data Roaming option. While it's not cheap it could prevent you from getting surprisingly high foreign data roaming charges.
There are several prepaid phones and plans that will work in Mexico, some are preferred over phones from the above Postpaid carriers.