Just returned a week ago from Cancun. We rented our own car and did a lot of day trips on our own. Never once, did I feel threatened or scared. However, driving there is an adventure and there were times that I found myself slightly nervous. The people are extremely friendly, staff at hotels and restaurants are wonderful, but not much English is spoken. Although we had a terrific time, I'm not sure that I would return anytime soon, but not necessarily for safety reasons. There are so many other places to visit that we try not to go to the same place twice (except for Hawaii and WDW).
The main reason we picked the Cancun area was that there was so much to see and do beyond the resort. I can't stand to just sit on the beach on a vacation and don't want to be tied to tour groups.
As others have said, if you stay in the tourist areas, or even venture out as part of an organized tour, you shouldn't have any problems.
I planned this vacation in February and between the swine flu and drug cartels, we considered changing our plans many times. I'm glad we didn't. However, if you are really uncomfortable, I would go elsewhere. Being scared and nervous is no way to enter into a vacation.