alexithymia (ay-lek-suh-THEYE-mee-uh) - n., difficulty in experiencing, expressing, and describing emotional responses.
Specifically, one's OWN emotions, though alexithymics also typically have trouble identifying the emotions of others. It's not that they don't feel emotions, but that they have trouble describing them except in terms of somatic sensations or behavioural reactions: "my face is warm" rather than "I'm embarrassed." Alexithymics often have trouble differentiating between different emotions that produce the same types of arousal. Studies suggest (per Wikipedia) that somewhat less than 10% of people experience some form of alexithymia. The word was coined in 1973 psychotherapist Peter Sifneos from Greek roots a-, not + lexis, word, + -thymia, feelings, passion -- literally, "without words for emotions."