Taditionally, according to the old comic books, divers carry knives that are almost swords, and use them to fight off the giant octopus and free themselves from huge clams. In reality, the popular trend is to have a tiny, doubles-as-a-toothpick type knife, since everybody knows we only carry the thing to cut line if we ever get free.
I played traunt from this school of thought, and bought a six inch bayonet blade. My main reason for this was that it wasn't just a knife, it was a multi-tool. It has a smooth edge, a serrated edge, a net-cutting notch, and it can also be converted into scissors.
When it comes to cutting just about anything you're likely to encounter underwater, scissors beat knives hands down. They're not nearly as macho and sexy, but they're still better. Which is why my spare cutting thing is not a small knife, but a pair of trauma shears, which cost me about £2.50. These things cut through ANYTHING - I've seen them cut through coins and D-rings, and they go through webbing like it wasn't there.
My knife lives on my waist strap, it's sheath attached by a few bits of line. My scissors live in my left pocket.
