I had some lock failures on folding knives years ago that where pretty bad: one in particular cut right down the center of my thumb and stopped on the bone. However, nothing that ever got stitches (super-glue and tape all the way!!).
The only cut that actually worried me was a couple years ago cutting mango. I was cutting around the pit and I had the mango on it's side and knife horizontal. With my left hand I was rotating the mango against the knife and, my grip on the mango slipped a bit. Like a fool, I was in a hurry, rushing and gripping the mango too low (below the plane of the blade). So, when I slipped, the right (outside) side of my left index finger smacked against the edge of my knife. -fast but not hard. Barely even felt it. It was a weird diagonal cut along the side from the crease of my first knuckle almost up to the tip, and clear down to the bone. Bled like crazy... so much that I had trouble getting the glue to set. I gave up and for the first 48 hrs I just flushed with alcohol, packed it with neosporin, and wrapped it with gauze and electrical tape. The thing that concerned me though was that I had weird nerve and tendon pain. Even a week after it would hurt if I raised my arm past a certain point or moved my forearm or wrist in a certain way. But, it eventually did heal very cleanly, with no permanent damage aside from a scar that's only visible under the right light and if you know just where too look.
That's the thing about all of my bad cuts: done with very sharp knifes and kept very clean, so no cool scars.
I very rarely cut myself, but my most common cut is actually more of a "poke" when rotating to a new knife or learning a new blade where my brain has not yet programmed in a longer length, my left hand occasionally gets a couple mm of tip that it didn't account for stuck into it, but a drop of super glue and 30 seconds of pressure and it's like it never happened.