There are two main purposes for using colored text in documents: style (make the document look more visually pleasing or adequate to its context) and readability (help the reader to understand its meaning). For hyperlink colors, one also has to distinguish between digital and printed documents: the special meaning only makes sense in digital.
Regarding style, less is usually more. Documents that use a coherent and clear color scheme, based on one or two main colors, just look nicer and more professional. It is also easier to align one or two extra colors with some corporate style to match the occasion. I would therefore not suggest to use different colors for different link types.
Regarding readability, blue-ish colors seem to say "link" for most people. Yet, I think that consistently used (dark) green or (dark) red would also convey the message that there is "something special" there. You can see the same color pattern on web sites: most use some form of blue, but others have their own style. For most documents, hyperlinks are an optional feature, so there is no big loss in readability for readers who do not understand the color. If hyperlinks are consistently used for certain keywords, then the document might still make sense in print, i.e., it should not be confusing to readers why some text is in color (or shade of gray if printed monochrome).
I do not think that the reader usually is interested in the distinction between link types, other than for internal link (to document) vs. external link (to some URL). It makes sense to distinguish this, but for all documents that are also meant for printing, one has to include the URL for external links anyway, which should be clear enough to understand that the link is external.
Regarding choice of colors in general, I suggest to avoid "pure" colors like #0000FF. They look too glaring (and also have disadvantages when using projectors, which sometimes are "weak" on one color). Look at this very website to get better examples: the link color I see is #145680. I find the named color MidnightBlue from the xcolor package to be an acceptable choice in LaTeX, which I prefer over NavyBlue. Also, keep in mind that the color should have sufficient darkness: light colors often appear to have more style, but are harder to read in print – the infamous devil's CSS #666 is used for text on many "stylish" websites. The same goes for some versions of blue that you might consider, especially when printed in black and white.