General security concerns about Cancun, Mexico

Mexico is a great place, and for the most part safe. Obviously you should use common sense, but you will be fine. The resorts and tours are also safe, so enjoy yourself.

I lived in southern Mexico for a couple of years and never had a problem (I'm a tall, blonde, white American), Mexicans are very friendly. I do speak Spanish though, and have always felt that this helps people warm up to me.

So, 

• learn some Spanish and be friendly
• Avoid obviously dangerous areas, and carrying valuables like Peter said
• Know travel regulations

If it makes you feel more comfortable, plan your whole trip out ahead of time and stick to the touristy areas

Have fun!

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 community.

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".

Before I visited Mexico for the first time, I also heard many stories about how dangerous it is, especially from Mexicans living in L.A.

Then I spent three wonderful months all over Mexico without anything bad happening to me.

I consider the part of Cancún where all the hotels are an even safer place. There are only hotels, shopping malls/restaurants and the beach. And it's full of tourists. Nice beach but boring. Cancún town proper is much more like a normal Mexican town and still perfectly safe in my experience, but I haven't been there late at night.

Use common sense when going out, don't take your valuables or any bags when going out at night.

My experience with Mexico is if you try to find trouble, trouble WILL find you. I have been to Cancun (Playa del Carmen actually) and there were lots of tourists and also military police (they call them Federales). If the AK47 isn't any indication, then you know that they don't mess around when it comes to breaking the law. I have been to Cabo quite a few times now, and there's been some security concerns there as well. I stay away from Cabo San Lucas because of how its crazy busy and the loads of people there. We stay in a smaller town called San Jose del Cabo and the scariest time was February, 2012 when Hillary Clinton (then USA Secretary Of State) showed up for a pre G8 meeting and stayed at the resort next to ours. There were Navy ships patrolling the shore line, military helicopters flying around and if that's not scary enough, there were Armored Personnel Carrier's (APC) all around the hotel. There were also metal detectors for anyone leaving or entering the hotel. However, nothing has happened to us so nothing is preventing us from going back again. I also don't go out clubbing or bar hopping late at night because that is where the pick pocketers and druggies go. Some friends went out to a club in Cabo San Lucas and even though they carried their purses with them wherever they were, someone managed to sneak up behind them and take everything out of it without them even noticing.