The obvious things are tones like different ranges of black, metallic hues, flourescent colours, etc... Things that are reasonable (possible pricey) to specify for print, but that are outside of the normal CMYK range. But in print, if you want a nice, clean, even colour, you want a dedicated ink for that. You don't want a dithered print. Look at a cereal box corner sometime - there's usually a registration print with little color samples. You'll see the usual CcMmYK colors for the bulk of the printing, but you'll almost always see a handful of pure colors as well. These are the registered pantone colors that get their own dedicated ink on the presses. You need this if you want your logo to be a solid color, even up close. Otherwise, you'll have that mess of various tones, pixelated, and imperfectly aligned.