A blogger at the Harvard Business Review has come up with the interesting back-formation "mentee", meaning the recipient of a mentor's care. I would not expect HBR to copy edit its blogs, but this came to my attention via Bloomberg Business Week and an Association for Computing Machinery Career News digest, both of which passed "mentee" right along.
The expression has apparent symmetry to recommend it. On the other hand, it looks like "manatee" at first glance; then it sets the mind searching for the verb stem "ment", which leads directly to "mentir" and "mentior", probably not what those who speak earnestly of mentoring intend; finally it suggests that the writer cares nothing for or knows nothing of etymology.
I suppose that if I had to write on the topic I would use "protegee", though one expects a mentor to instruct as well as protect.