Undead is a term used to describe those that are officially deemed deceased, but can still interact with the living of Arda. In the Third Age, "Dwimmerlaik" was often used to describe any undead beings.
Some of the most notable examples of this dwindling race in Middle-earth are the Nazgûl, kings of Men, corrupted by the influence of the nine Rings of Power, and made loyal to the Dark Lord Sauron, and his One Ring.
Celebrimbor, a wraith, and Talion, a Ranger, inhabit a single body, after being, respectively, merged by a blood ritual, and being the victim of said ritual. That being said, Talion and Celebrimbor are considered one undead being.