Seeing as how the three primary colors are cyan, magenta and yellow (CMY), why do monitors and almost all the GUI components out there use red, green and blue (RGB)? (If I'm not mistaken, printers use the CMYK model.)
Is there a historical, hardware/software, or other reason for it?
There's a difference between additive colors (http://en.wikipedia.org/wiki/Additive_color) and subtractive colors (http://en.wikipedia.org/wiki/Subtractive_color).
With additive colors, the more you add, the brighter the colors become. This is because they are emitting light. This is why the day light is (more or less) white, since the Sun is emitting in almost all the visible wavelength spectrum.
On the other hand, with subtractive colors the more colors you mix, the darker the resulting color. This is because they are reflecting light. This is also why the black colors get hotter quickly, because it absorbs (almost) all light energy and reflects (almost) none.
Specifically to your question, it depends what medium you are working on. Traditionally, additive colors (RGB) are used because the canon for computer graphics was the computer monitor, and since it's emitting light, it makes sense to use the same structure for the graphic card (the colors are shown without conversions). However, if you are used to graphic arts and press, subtractive color model is used (CMYK). In programs such as Photoshop, you can choose to work in CMYK space although it doesn't matter what color model you use: the primary colors of one group are the secondary colors of the second one and viceversa.
P.D.: my father worked at graphic arts, this is why i know this... :-P