Quote from hilojack:
Well I'm not the OP but was an advocate of Cozumel. Believe me when I say Cozumel is nothing like the rest of Mexico as far as crime is concerned. And I understand your reservations about crime there having been to other parts of Mexico as well. The reason crime is non-existant there is because 1) it is an island-- there really isn't anywhere to go 2) the island's only source of revenue is tourism, and they go to extreme lengths to protect their reputation 3) there is both a naval and an army base on the island, and they also act as de facto police 4) the people are just nicer-- not the chilangos (refugees from mexico city whom some blame for the problems) that you encounter on mainland mexico.
here's a true story that happened when we were there. My girlfriend at the time who went down with me (now my wife) and one of her friends were out jogging in the late afternoon when they encountered a flasher. My wife was initially scared but her friend was laughing telling the offender that it was pequeno. When they relayed the story to our other neighbor (a local woman), she called the police immediately. Within 10 minutes a truckload of cadets from the army base pulled up and scoured the area and caught the guy and hauled him off. The captain then proceed to apologize to the girls profusely and insisted that we visit his brothers restaraunt where we were treated to an evening of free booze and food.
Bottom line is anywhere you go where there are impoverished people, you will have some sort of criminal element. The important thing is how they deal with it and whether it is more prevalent than not. In cozumel's case, we couldn't have felt safer.