6 right now. Probably had 20 or so total since I started. I generally don't hoard strops like I do most things (soap, razors, stones, brushes)... probably because they're hard to find in good vintage condition at reasonable prices. It happens, but often a nos or nearly vintage strop sells for MORE than a similar quality modern... and restoration can be a lot of work on slightly damaged ones, and people LOVE hiding serious damage with bad pictures on eBay. Just a really high risk, high work, low reward thing to collect in my experience.
That said, I've got a Dubl duck, a Pearl duck, a Freeman 588-x, a "Moose" shell, and an Ambrose and a Kanayama. First four are vintages.
Currently have 4, 2 Vintage illinois strops 6452's,1 modern Illinois russian, and just got the one shown in the picture below (koken scotch shell). Im still working on conditioning the Koken slowly. Wish I could get the wave out of it tho.