I don't carry a knife, but do always have a cutting tool or two. In recreational diving, the most common entanglement hazard you can encounter is monofilament fishing line. For cutting yourself free, or cleaning it up to avoid the hazard for other divers and marine life, surgical shears or a safety cutter are all you need (I like the eezy cut trilobite). Cheap, easy to care for, and safe to use. Less risk of accidentally cutting you, your gear or your buddy.
I keep the safety cutter attached to my low pressure inflators hose on my shoulder and shears in my BCD pocket.
Shears and safety cutters are also easier to fly with - they can go in your carry-on luggage. Many marine parks won't allow you to carry knives, but will permit shears and safety cutters.