I think the OP was talking about very large, global knife companies who make bladed tools the average person is likely to have in their house or pocket, rather then enthusiasts products in the upper price range.
There are only a handful of them, the ones I can think of are Victorinox, Leatherman, Mora, Opinel, Case, Buck. In that order. Maybe the likes of Kershaw, Gerber, Schrade, CRKT & Böker. Excluding kitchen knife or axe/saw brands. Case & Buck are only very well known in north america, elsewhere I doubt most will know about them or own one, but maybe I'm wrong.
Most people don't spend more then $20-$50 on a knife and likely wont know what a Chris Reeve is, and I'm willing to bet most wont even know about Spyderco or Benchmade, especially outside the US.
Out of those Brands, my pick is Victorinox. Not even a contest. The put quality swiss made tools in the hands of the average person, at affordable prices. Truly the everyman's knife. Plus they make just about everything, and a pretty good version of it to boot.