I sharpen on either diamond stones or my Burr King

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I find the most useful thing about stropping is that it wipes the wire edge off after sharpening. After that, "stropping" is kind of like "sharpening" - depending on what setup you have and what technique you use, you can get a wide variety of results, both intentional and otherwise.

Shaving edge, scary edge, spooky edge, working edge - you can strop to all of them, once you figure it out. At this point the only things I don't strop as a matter of course are axes and machetes, and even they benfit from it - it just doesn't tend to be worth it given the steel quality and rough use.
My quick n dirty these days is work to a wire edge on a 600 grit diamond stone, then use a flat leather strop rubbed with 'white diamond' buffing compound (which contains no diamond) to finish - when the wire edge is gone to the touch, it's done. Thick soft leather, or stiff hard leather, and heavy valve grinding compound, or a light jewelers compound like Zam, can give faster or slower results, finer or coarser, more convexed or flatter, etc.
Just before I moved I picked up a 2x72 strop belt for the Burr King - when I get the shop set back up I'm real interested in seeing how that works out. It's not the Hand American, it's the one Sheffield Knifemaker Supply sells, for about half the price.