James links to a very good post on the subject of knife 'fighting', well worth reading. Especially the quote noted by James:
As far as your attacker is concerned this is not a fight, it is an assassination.
I'll throw in another quote I heard from someone years ago:
In a knife fight, the winner goes to the emergency room.
Way back when I was playing in the SCA, one day at a tournament there was a 'side-issue' of a trophy for knife-fighting. Basically dueling: two people in a ring with wood and/or foam knives, see who scored first. Very little to do with a serious "He's trying to KILL me!" fight, but it did point out a few useful things. Like the fact that it's almost impossible, facing off with another knife-armed somebody, to be able to cut them without getting cut yourself. And if you honesty assessed where you got cut, it was easy to see that even if you won you'd be looking at anywhere from stitches and blood loss to crippling injury. I managed to take out a guy who was ungodly fast and good, basically I surprised him; but I'd have been cut on both upper arms doing it, see the above noted injuries.
Would I carry a knife as a primary means of self-defense? Only if I had no other choice.