I just did my cavern class a few weeks ago, and my instructor really hammered us on this. Here's how he told us is breaks down:
95% of all cave diving deaths were people who were not properly trained in cave diving.
Approx 4.5% were due to a failure to run a continuous guide line.
Of the remaining 0.5%, every death with the exception of one or two, was due to either violating the 1/3 rule, diving deeper than 130', solo diving, or (in two cases) not having enough backup lights.
I realize, before anyone calls me on it, that you don't die when you hit 131', or when you dive alone, or when your light goes off. The point was that if you have proper training, run a continuous line, follow the 1/3 rule for air consumption, stay above 130', dive with a buddy, and have a minimum of three lights (a primary and two backups), and you STILL die, then that's pretty much God just striking you down.
Pretty safe IF you're properly trained and prepared. Of course as we all know, almost 50% of all statistics are made up...