What everyone else said, always, always, always report accidents, even if it's something small, like a paper cut. One of my college instructors had told a story of her dad getting a paper cut and dying from it.
Worker's comp is insurance that is readily available. If you don't need it, then fine, but if you do, and you don't report it, then guess who's footing the bill?
I would be in so much debt if it weren't for worker's comp. I've had 2 worker's comp cases, both of them requiring major treatment. One was a torn ACL, needed reconstructive surgery, 5 days hospitalization, and 3 months of physical therapy. The other was a back injury. Many different treatments (steroid injections, nerve tests, etc. etc.), at leat 9 months of therapy, 4 or 5 different specialists. I would be in serious trouble if it weren't for worker's comp.