It is the 3rd winter I spend in Mexico. Is it safe? It depends. If you do not visit the wrong places, most probably nothing bad will happen. Let me give you an example. This year I and my girlfriend travelled more than 3000 kilometers hitchhiking. We did not even have one uncomfortable situation. On the contrary! It was amazing! People invited us for meals during and after the trip. Once we were even given accommodation to stay for a local festival called Xantolo. Which is equivalent of the day of the dead.
There are some areas though which are not very recommended. Especially in the North. I have not been there mysefl so far, therefore I am not able to give you the first hand information on that region. It is always a good idea to ask some local person for more details.
At the moment I am staying in Playa del Carmen, at the Caribbean Coast. It is located about 70 km south of Cancun. If you come here, you will find it very safe. And soooo much different from the rest of Mexico. It is full of hotels and restaurants. It is among one of the fastest groving cities on the planet! You can see construction almost on every corner!
At the same time, the beaches and sea are breathtaking. In my opinion it is one of the most beautiful places I have visited.
If you decide to come here, you risk two things. One is that you will fall in love with this place and decide to stay (as many of my friends did). And the other that when you finally decide to buy a bicycle to move around the city faster it will be stolen... Unfortunately it happens too often here. But that is basically it.
So if you are wondering if Mexico is safe - my answer is: YES, it is. Just have your eyes open and you will be fine :)