Umm...eight. Assuming I don't have a backpack on me as well.
My main "go-to" knife is an older S&W, from back when they were of better quality than the newer stuff, their original SWAT model. I'm looking to replace this, ideally with an Emerson CQC-8.
I also carry a Becker BK-11 dangling from my neck; a 5.11 Tactical boot knife, in my 5.11 boots; a Gerber Ripstop, the smaller version, in an EDC pack (by Maxpedition) in a cargo pocket; a Leatherman Style CS, with a 1.6" blade, which is attached to my keyring; a Leatherman MUT, which, despite its specialized intended purpose, still makes a pretty good EDC multitool; and, finally, a Sinclair Cardsharp.
Hmm...that's only seven...I'm pretty sure I once counted eight, I might be forgetting one!
You can also typically find 3-4 flashlights, 3-4 pens, a small assortment of minor medical supplies, surface sanitizing wipes, hand sanitizer, duct tape (wrapped around a used gift card, so it's flat), paracord, a P-51 can opener, a WD-40 pen, and a few various other odds n' ends on my person. Oh, and a Leatherman Raptor, a folding trauma shears, which I don't include in my count of knives, since it's more akin to scissors (and although it does have some other rescue-specific tools built in, Leatherman has rightly decided to not include an actual knife blade on this multitool, to keep it focused to its purpose; it doesn't even have a bottle opener, which I thought was a universal law that all multitools must come with!).