I have arrived just recently in Mexico City planning on traveling many months, so this information is based sole on conversations with people here and back in CA who travel here regularly, and from reading probably 5-10 articles on the internet.
My understanding from a friend who travels to mexico commonly is that there are a few important places to avoid, specifically those are the northern boarder towns and Sinaloa (in the central/west part of the country). The southern regions are generally safer areas, and any larger cities tend to require typical awareness that you might expect to have in New York, LA, or the like. Most of the serious violence reported in the media coming from the drug trade is occurring outside of the major city centers. If you are traveling to rural areas you should be prepared to do more research beyond what I or others will say here.
If you are traveling to tourist destinations then read up on wikitravel for a few good tips on finding the right taxis, safety tips for the area, and ask for information from your hotel about security. I would not expect that if you are on vacation that you are likely to encounter major problems beyond what is typical of traveling the area. As with any trip to a less developed nations, do a little reading in a guide book or online and be aware of your surroundings. Don't get completely drunk in an unfamiliar part of town. And know how to call a taxi before you go out for late nights.
It is my opinion (and this is only one persons opinion) that the major warnings coming from US border patrol are coming on account of the escalating drug problems. I think these problems probably affect individual ground travelers, and individuals in specific locals and rural areas. For those flying to a tourist destination the warnings are probably less critical (though not to be ignored entirely).
I have not personally heard of the problems targeting foreigners specifically, rather that you simply don't want to be caught in the cross fire, regardless of whether you're foreigner or local.