Jacob being offered an incanted cup of wine by his mother, to make him ageless. ("Across the Sea")
Agelessness is the supernatural lack of aging over time. While it protects those who possess it from growing old and possibly protects them from disease, it is distinctly different from immortality in that ageless people can still be killed by other means.
Four characters are known to have possessed agelessness: Jacob's adoptive mother, Jacob, and Richard Alpert. The Man in Black had the ability to take on the form of deceased people, making him appear ageless. Jack Shephard may have briefly gained the ability after becoming the new Protector of the Island. Hurley may have as well, and Ben may have after becoming Hurley's deputy.
Ricardo being touched by Jacob, causing agelessness. ("Ab Aeterno")
Jacob's adoptive mother appeared to be the same age for at least 43 years until she died. Shortly before dying, she recited a incantation to Jacob, who lived for about 2,000 years without aging. ("Across the Sea") ("The Incident, Part 2")
Ageless JacobThe protector of the Heart of the Island held an advanced form of agelessness.
In 1867, Jacob, with a simple touch, made Ricardo an intermediary between him and the people he drew to the Island. Ricardo, later Richard Alpert, used his agelessness as a tool to form and help advise groups of Others for Jacob's tests of humanity.
Richard remained the same age for at least 140 years, and was unable to kill himself but could have been killed by other people. ("Dr. Linus")
Richard did not age during his tenure under Jacob. ("Ab Aeterno")
After Jacob died and Richard was no longer his advisor, he started to age normally. ("The End")
Ben Linus later became Hurley's "number two," although it is unknown if he received agelessness or completed his task while aging normally. ("The End")
The Man in Black
The Man in Black, while not strictly ageless, often assumed his original form during his thousands of years on the Island. ("Ab Aeterno") He also appeared in Christian Shephard's form for three years before ending his life currently in John Locke's form. ("The Last Recruit") ("The Substitute")