Feel free to add any razors you know of that use special blades. Wardonia (most Wardonia razors only take Wardonia blades) King Oscillator (can be used w/ a regular blade but no oscillating) Durham Duplex Segal Ronson Enders Valet (Feather makes modern Valet blades)
Christy. Burham 1909 SE (although regular SE blades kind of fit) Dime razor. Not sure if a regular SE can be made to fit or not, but the original blades are a bit different. Band razors such as the Gillette Techmatic and Schick Auto-Band. All sorts of cartridges, but I take it that we're not really talking about that. And a special situation. Gem Micromatics take regular SE blades, of course, but at one time Gem made special double-edged blades that would fit only the Micromatics. Only one edge was exposed at a time. When it went dull, you opened the razor, and turned the blade around.
Cool. It sucks buying razors and not knowing it takes special blades. Then you look around and they tend to be very expensive.
1950s Playtex hair trimmer. Picture a Durham-Duplex straight style razor that's also adjustable. I've considered trying to shave with it...they came with pretty sharp stainless blades so it might could be done.
Apollo french razor. Uses curved blades. Fémirêve french razor. Uses concave/convex edge blades. Keen Kutter.
I forget the name right now, but there was a women's armpit razor that looks like a small umbrella and took circular blades.
There are some in this thread: http://theshaveden.com/forums/threads/safety-razors-i-wish-could-still-be-used-more-easily.42377/