I'm not quite sure why, but I have an affinity for characters that are somewhat mysterious or secretive. That's not to say I like characters who are double agents or who conceal themselves for nefarious purposes. Oh no, it's the shy characters or those who are hiding something out of necessity that I find the most intriguing.
Take for example the poster below:
Yes, it is Jenny Wakeman (or XJ-9) from the Frederator series My Life as a Teenage Robot. Notice how she is in silhouette, which adds even more mystique to her figure, as if the shadow is concealing something about her character, which of course it is (hint: she's a robot).
There are plenty of other example throughout the animated universe, too many in fact, to list here. However they inhabit various places in TV shows and films, from protagonists to sidekicks to members of the supporting cast.
They add a lot to any show or film for a simple reason: they make the audience think.
Mysterious characters represent a discord with their surroundings of which other characters may or may not be aware of. In any case, the audience is almost compelled to put the pieces together or to speculate on the reasons behind such circumstances. Much the same as Lisa Simpson mulling over the enigma that is Nelson Muntz and why that make him even remotely attractive.
This is the key to why I find them so interesting, they give me something much more than the performance on-screen and in so doing, increase my enjoyment immensely.
Another great example is Megara from Disney's Hercules.
A wonderfully complex character who hides a secret from the hero that is hidden for much of the film. we are forced to guess the reason for her connection to Hades for quite a while as we are kept guessing her motives. Only once they are revealed do we see and can appreciate the complete character for who she is.
Initiating thought within the audience is a key way to maximize their enjoyment. Mysterious characters are a superb way of doing that because they allow for the audience to both connect with the and to ponder the character in a way that is outside what is presented on-screen.