When I did my Instructor Development Course a few years ago my Course Director made a great point. One of the instructor candidates was geared up and ready to get into the water. The Course Director stopped him and asked him where his knife was. The candidate replied that he didn't always carry it when he was diving. The course director, in his best exaggerated "teacher making a point" voice told him "you are a certified diver and you are my dive buddy. You have a responsibility greater than just to yourself, you have a responsibility to help me if I get into trouble. I have enough respect for my buddy to carry a knife to help him. Show responsibility and respect for me, put your knife on"
I carry the Atomic Titanium Ti6 knife because it will never corrode. I also carry a pair of EMT shears (for stainless leader) but going to upgrade to the Dive Rite Titanium Shears, and on my BCD shoulder I carry a small Dive Rite Z-Knife (line cutting tool). When spearfishing I carry the Riffe Silencer with a teflon coated blade specifically for fish.
It's apparent from the replies on this thread that most of the experienced divers, and even most of the newer divers, understand the importance of wearing at least some type of cutting device