A great moneysaver is to deactivate your mailbox. Otherwise, if someone calls you, you have to pay for recieving a call, then the phone redirects the call to your mailbox, and you will be charged again for an outgoing international call to your mailbox. If you own a fancy shmancy smartphone, also check the International Data rates or disable any Push-Services... that could be really expensive. Better check with your local cell phone dealer, or you cell provider.
Make sure that all of your calls have been put on your bill before you disable the international calling upon your return home. It can take weeks before the charges are added. If you do it too soon, you may get charged crazy rates.
Actually if you do not answer the phone when a call comes in there is no additional charge for that since your voice mail is saved wherever you are originally located and there is no charge for that. But if you call the voice mail to check the message you will use roaming charges and the international rates. And no this is not expensive. Verizon for example charges $65 for internation data vs. $30 for domestic only. You can call the night before you leave for Mexico have them turn it on for you and then deactivate the minute you get home. The rate will be pro rated to whatever you actually use data wise for the time you are outside the USA.
We have AT&T just called a couple days before we left for Cancun and had them put the international plan on and didn't have any problems other than it took forever to send a picture message.
I would love to! But I think if my Mom couldn't get in touch with me she would come down there.. better to talk on the phone