I'll remove any hook I can if I feel I won't do any more damage to the fish. On the east side where I fish we are restricted to barbless hooks, so if a fish is hooked in the eye or eye socket, I can remove it without further damaging the fish. About the only time I leave a hook in is in the event I hook one in the gills, as even with barbless hooks there is a chance of causing the fish to bleed, which I try to avoid. When bait fishing, I happen to like barbless hooks even if I'm not required to use them as it makes dehooking much easier. I lose very few fish as a result of going barbless.