Not counting Leatherman tools, four.
Mine are all small and have different purposes, though, so I don't think it's particularly excessive.
1. Boker KeyCom (1.5" blade, entire thing about the size of a USB thumb drive) - clipped to my right front pocket, with a small flashlight hanging from it. It has a very usefully shaped main clip point blade and is suitable to a number of quick little cutting chores.
2. Victorinox Alox Cadet. Just an ideal overall pocket tool kit. I use the other tools on it probably more often than the knife blade, due to the overlap with the Boker, but it does get used and keeps a very sharp edge.
3. In my bag, in an Altoids-tin mini first aid kit, a Victorinox Classic SD. Small blade, scissors, tweezers, toothpick. Essentially a minor first aid tool. I haven't used it in ages, but it's there nestled in along some bandaids, gauze pads, and adhesive tape just in case.
4. Also in my bag, in the bottom of one of the pockets, is a Case Slimline Trapper, stainless steel blade. This is my dedicated food prep knife, for those infrequent occasions when I need to cut up an apple, sandwich, whatever. It makes a great food slicer and takes up almost no room. Since I use it for nothing else, I never need to worry if it is gunked up with packing tape glue or dulled from cutting cardboard.
So there ya go. Four knives, four different purposes. All small, all non-threatening. Two in my pockets, two in a bag I carry to work. Some overlap, sure. But not enough to where any of them are especially redundant. If I gave up any one of them I would lose functionality that the others would not fully cover.