Mahavatar Babaji - an immortal.
Widely written about in sources such as "Autobiography of a Yogi" by Paramahansa Yogananda. Said to have maintained a physical body for at least two thousand years, many people including identifiable contemporary figures such as Leonard Orr (father of the Rebirthing movement) claim to have met him in the physical world, just like they would meet any other people. A large and colorful leaderless cult surrounds this figure. Don't believe anything they say!
Babaji is said to be manifest physical bodies at will and to frequently operate in the physical world by creating amazing chains of "coincidence" which lead followers (or those who's life he wishes to interfere in) all over the world, bringing them into contact with spiritual wisdom, true love, or their life's work.
Also known as Shiva Baba, Almora Baba, Haidakhan Baba and many other names. The guru of Gurus.
http://www.crystalclarity.com/yogananda/33.asp has some of Yogananda's writings about this figure.
http://www.rebirthingonline.com/Babaji/picturegallery.html Various pictures of the Haidakhan Baba.