This is likely to be closed quickly, or turn into quite the nasty debate as many people have different opinions.
I personally carry a knife, or three. It all depends. I would rather have a nice large fixed blade ready for action but it isn't always an option. Sometimes I go with a smaller fixed blade. Usually everyone carries a folder, I try to do the same. I can't carry a firearm in CA. I like to have a knife weak side just in case, and I practice for it. Knives are good tools for cutting someone off of you if they are stronger, choking you from behind, holding you down.
The main issues are:
1. Distance to the threat must be close and no one wants to be there.
2. One must know what they are doing and have empty hand skills to assist.
3. One must know 100% they are in the right, knives are more likely to make you look like a criminal.
4. While guns aren't man stopping machines, knives can be worse.
5. Diseases that spread through blood can get to you easier.
Anyone attempting to use a knife against someone with a gun needs to be close and needs to stay away from the muzzle. This should be practiced and drilled, not just alone but with partners. The knife you carry needs to be sharp, and hopefully opens easily and locks well. If you have to use a folder, practice opening it under stress. Don't worry so much about getting the weapon out, transition from empty hands when appropriate. Against a knife, another knife is a bad idea.
I'm a bit sick, I hope I got my points across. All the important ones anyway.