Well, gee...what kind of razors are there?

Man is an ingenious creature. I reckon the very first razor was nothing more than a sharp-edged rock or seashell. And look what he's advanced to...

heh.

Sure, there are a slew of multi-blade cartridge razors out there, but how many would be worth collecting? Let's stick with the most commonly-found classics.

Single-edge razors use a blade with one edge that's been honed; the other edge is sometimes covered with a narrow strip of metal (called a "spine"). You've probably seen single-edge razor blades at hardware stores, although they probably aren't what you'd want to shave with. Basically, the top (or "cap") of the razor flips up, a blade is placed on the base plate, and the top closed, exposing the single sharp edge. A variation of single-edge razors is the injector; each narrow blade is encased in a mechanical loader that is inserted into one side of the razor by way of a built-in "key". A slide forces a new blade into the razor while pushing an old blade out (if one is loaded). Some injectors are fixed (as far as mildness or aggressiveness), while some are adjustable (the blade gap can be set for both mild and and aggressive to a varying degree). Straight razors are also considered single-edge, but they're scary, and I don't wanna go there. 

Double-edge razors have blades with both edges sharpened. Razors are typically the three-piece (the handle is unscrewed from a stud on the cap, which protrudes through the base plate). The older models had two studs in the cap and used blades with three holes to keep the blade aligned. The slot and diamond pattern in the blades we use now came out around 1930. The other type of double-edge razor is the twist-to-open (TTO); a knob at the base of the handle is turned to open and close "butterfly" doors in the head, where the blade is loaded. Like the injector razor, TTO razors can also be fixed (but of varying degrees of blade gap, like the mild Blue-tip and more aggressive Red-tip), or adjustable (which can be sub-divided into Slim, Fat Boy, short and long Super Adjustable, and the rare toggle). There are fancy TTOs, such as Aristocrats, or Plain Janes like a flare-tip or a "40's style".

As you can see, you can get pretty involved with even one type, Like Super Speeds, for example, which began (by name) in 1947 (the 1946 Ranger Tech is considered the forefather; but if you include it, you may as well include the 1941 Ranger) through 1988. Here is an excellent guide to all that is Super Speed. And here is a good pictorial on classic Tech razors.