I think that incidents have definitely made me a better pilot. I have never damaged an aircraft through my own mistake (and I hope and work hard to continue that!), but have had incidents such as electrical failure, partial engine failure, and gear up landing (due to mechanical failure). I feel that the experience gained in handling these is immensely valuable for any future unexpected events.
Of course, I have certainly made mistakes; I've just been lucky enough, or caught them soon enough, that no damage has been done; and this experience too is very helpful.
It's interesting, though; we can't really induce real emergencies to pilots to help them learn, so is there a way to capture this learning over and above what is already done with regards to practicing emergencies in training? The level of realism achievable by airline simulators is currently out of reach to we GA pilots, but with the advance of technology, maybe not forever?