It seems like I'm always getting called upon for recovery efforts. Between my large winch and willingness to help out... I bet I've done probably a dozen just this summer alone. Typically all it's taken was my equipment and possibly an anchor to hook to my rig. Which are cable, and straps. But I did a recovery a few months ago that took even more. I used chains, straps, cable, snatch block, two winches, and three vehicles for anchor points - oh, and lots of big thick moving blankets!
The key to the recovery was being able to think clearly about how the safest way to do it is, without hurting people or rigs. Then going back to what everyone had in their tool boxes to see if we could make it work. Everything we needed, I have with me at all times. I just didn't have the quantities.
On the flipside, yes I use my winch a lot, and yes it still has cable - 7/16". After each use, it get's wound up and put away correctly. Even if someone has already taken the time to wind it up for me, if I don't like the way it's laying, I do it over. I've thought of going to rope, but the cost is way too high for a rope that can handle 33klbs (double winch capacity). My cable is a litlte over 2 years old and it's still in great shape, no freys or kinks, so I'll continue to use it. But when I do use it, I make everyone stand well away from it. I did when it was new, and I will continue.
I have seen a cable break. Nobody was killed, but when it broke, it wrapped around the guys legs that was running the winch and dropped him to his knees. On later inspection, it left two large raspberrys/burn/abrasion marks. I think he was lucky to only have that happen to him.... I've also seen the effects of the cheapy sewn in hooks on tow straps (Harbor Frieght stuff) and someone should campaign against them to pull their stock. They are lethal!!! One recovery I did about a year ago, they had some of these and tried to pull the guy out of the mud before I was called upon. Brand new Dodge 2500, one of the straps broke and now he has big dents on the top of his rig and the tailgate.