I haven't been to Mexico myself yet, but I've given this some thought recently, from the perspective of visiting Yucatán peninsula (incl Cancún) and maybe other places like Puebla and Veracruz. (Specifically, I've read news and blog posts, and talked with Mexicans and others who've been there.)
Here's a summary of my understanding (Nov 2012):
- How dangerous is it varies greatly from state to state. See for example the "murders per state" map here. Or this recent map by The Economist (22 Nov 2012); they compare the Yucatán state to Finland. (Though note that Cancún is not in Yucatán state, but Quintana Roo, and that Finland has a relatively high murder rate for an EU country).
- Currently it is best to avoid the northern parts of the country, close to the US border. Especially the state of Chihuahua and the city of Ciudad Juarez. This is also what several Mexicans have told me.
- Going to Cancún and elsewhere on Yucatán peninsula (especially Mérida and the rest of the Yucatán state) should be safe. A Mexican woman I talked to just two days ago said it's segurísimo (extremely safe) for a tourist to visit that area. This is especially true if you plan to stay in the tourist areas all the time, near your hotel and the beach (though otherwise I personally wouldn't recommend such boring way of travelling :-P).
- On the other hand, if you look for it, you will find some disquieting news from Cancún too. E.g. here or here (though those are a couple of years old).
- Mexico City is huge but actually quite safe. Both the stats and people I've talked to seem to agree on this.
- For other areas, do some research beforehand. For example Acapulco and state of Guerrero, though not near the US border, have seen considerable rise in violence in recent years.
If you want to follow news about Mexican gang violence (probably increasing your fears in the process), see the "Hell on Earth" blog.
Update: From the same blog, see this overview on security conditions in Mexico (30 Nov 2012), including a state-by-state assessment by the US State Department.
Quoting the blogger's commentary:
Despite what many think, much of Mexico is still very safe. Much of
the violence in the last year has isolated itself to border area
states and southwest Mexico.
Even border state, Baja California, has become safer than many U.S.
states, as well as Ciudad Juarez being on the path to a much safer
Typical tourist beach cities have seen little to no violence, Acapulco
being the exception. Major cities like Mexico City, Guadalajara, and
Puebla have escaped gang style violence for the most part, leaving
them still perfectly safe for the conscious business traveler.
Definitely good reading for those planning to visit Mexico. Specifically of note (for OP) is that for Quintana Roo and Yucatán states, "no advisory is in effect".