As a foreign tourist, you are unlikely to be kidnapped in Mexico. Understand that "foreign tourist" is an important qualifier. You are probably a tourist. Read on for clarification.
I am not saying kidnapping does not happen in Mexico. It does. I am saying that there is a big difference between tourists and locals. Don't confuse what happens to someone living in Reynosa with what might happen to you traveling through Guanajuato. Don't confuse what happens to foreign businessmen with you. Don't confuse what happens to people with relatives in Mexico with other tourists.
I am not saying nothing bad ever happens in Mexico. I speak from a little experience. I was mugged in New Orleans twice, shot at once. I was mugged 40 years ago when I was drunk in the red light district of Oaxaca. A Mexican man came to my defense. I kind of set myself up for that one.
"Kidnapping" is almost always thrown into any article about Mexico. If you have Mexican friends, they almost always know someone or know someone who knows someone who was kidnapped. And they are telling the truth. It does happen. Kidnapping mostly happens to locals who may not even be rich, just accessible. It happens to family members, who are sometimes from the USA. It happens to businesspeople. The one thing all these groups have in common is that for the kidnappers, they are easy to communicate with and they have an idea of what they are dealing with. With a tourist, they have no idea.
I've gotten impassioned mail from those whose family members were kidnapped and once had a discussion with a man who was victim of an express kidnapping. Things happen, just not all the time or very frequently. But when you are the victim of any crime, it's hard not to take it personally.
There are other forms of "kidnapping" that do affect tourists. Express kidnapping, where a taxi driver or other person takes you to the ATM machines for a few hours or even a few days, then lets you go. That happens in the USA too. It sucks, but it is statistically unlikely to happen to you. It does happen more so in the big cities. It happens in New York and Chicago and Los Angeles, too. If it happens to you, there is not a lot to do. You can call or go to the nearest embassy or report it to the police, but that would be for insurance and satisfaction. Don't expect anyone to be caught. IF you passport is taken, then you have to make a police report and go to a consulate or embassy.
I base my opinion on years of following stories about Mexico, traveling myself and the feedback of literally hundreds of thousands of Mexicans and American and Canadian tourists.
I have it on good authority (I know people who know organized criminals) that cartel soldiers have been ordered by their jefes to leave tourists alone whenever possible.
It is at this point that those who think they know Mexico better than I stop reading. They immediately fire off an angry, self-righteous missive to me. Please don't. I am trying to present a balanced view to the rampant negativity that you probably believe. If you feel that way, fine. There is no need to write me or even for you to go to Mexico. I am writing to the open-minded who are willing to listen to reason. You already have your opinion.
Businessmen are not tourists. DEA agents are not tourists. People with families in Mexico are in a different category and are treated as Mexicans in the eyes of criminals. So when you hear of an American who was visiting family in Mexico and was kidnapped, please try to understand the nuance. You don't hear of Mom and Pop from Des Moines being kidnapped.
Your chances of getting kidnapped in Mexico are slim, unless you are a really rich person and then you probably have bodyguards. Overall, your chances of having something bad happen to you in Mexico are slimmer than in the United States. There are certainly more murders in New Orleans or Houston than any comparable Mexican city.
However, getting robbed or abducted while using an ATM is something everyone should worry about. Should this happen, the abductees are held for 3 days and forced to use the ATM to withdraw money. That happens in the USA too. If you are unfortunate enough to experience this, your best chance of getting away is to do it right away. That may be easier said than done. Some people have thrown their wallets at their assailants, which distracted them long enough to get away. Fighting with them could be dangerous, but if there are any other people on the street, screaming is your best defense.
I recently engaged in a civilized dialogue with a gentleman who had encountered a rogue taxi driver in Puebla and he and his girlfriend were detained and forced to use their ATM cards. They cooperated and were released unharmed after a few hours (which no doubt hardly seemed "a few" to them). Stuff happens, as I have always said. It happens everywhere and you just have to be aware and careful in cities, as you would anywhere.
Just be as careful, or more careful, as you would back home, i.e. watch who's around you in a city, especially when using an ATM, don't take gypsy cabs. Even with regular cabs make sure there is only 1 person - the cab driver - in it. Don't flash a lot of money and probably nothing will happen to you. In smaller towns, you are much safer in Mexico than in the States. In cities, you are probably safer too, but just be realistically careful. It's probably not a good idea to drive your Ferrari or BMW to Mexico, although you will see a few driven by local rich guys and gals.
All that said, well-to-do Mexicans do worry about kidnapping. It happens. But it doesn't happen as often as the media would have you believe. They know the precautions to take, but their situation is not the same as yours, as a tourist or a gringo expat.
Ask anyone who knows anything and he will tell you that children are ten times safer in Mexico than in the USA. Yet, I get tons of questions abut whether it is safe to take children to Mexico. Absolutely yes. In smaller towns, kids still play in the zócalo after dark. While there are perverts in Mexico, there don't seem to be as many of them. Mexico is a very kid-friendly country.
However, the times, they are a changin'. I'd pay more attention to children today than even ten years ago. There is no reason to be paranoid, but prudence has a delightful sound to it.