An egotist is an extremely self-absorbed, bragging person. If you share some bad news with an egotist, he'll be most concerned with how it affects him.
Egotists believe that the world revolves around them — when an egotist reads the newspaper, the stories that concern her most are the ones that involve her own interests. You might have a hint that a new acquaintance is an egotist if he uses the word I constantly during your conversations. Egotist was first used in the 1700s, and it initially meant specifically "talking too much about one's self," from the Latin ego, or "I."