Oracle

The Oracle is a strange woman who lives atop Ice Mountain. She is an important figure in the Dragon Slayer quest, as she provides a clue as to how to access one of the map pieces. She is also involved in Perils of Ice Mountain, where she foretells of a day when the Kharidian desert will reach Varrock and Falador if the player does not repair the environmental damage caused by the Dwarven Power Station. During that quest, the tent in which she lives is damaged in an avalanche, though it is repaired by the player. Occasionally, she will be visited by Postie Pete and, after completion of The Chosen Commander, Zanik as well. One of the Wise Old Man's tasks involves taking a message to her.

Original Purpose
According to a posting by Andrew in June 1999 (one of the first references to his RPG):

Dialogue
When spoken to, she says a wide variety of one-liners. These range from bizarre advice to warnings and hints. She spoke of the Stone of Jas long before While Guthix Sleeps or even Meeting History, where the stone is first seen. She even makes references to the dragonkin and Juna, as well as comical phrases such as, "if a tree falls in a forest and nobody is there, nobody gets woodcutting xp."

Trivia

 * Originally, the Oracle was a man, however in June of 2007, he was given a tent, a graphical makeover, and turned into a female. Therefore, the Oracle was the first NPC to switch gender (excluding the Makeover mage, who switches gender periodically). In RuneScape Classic, the Oracle is a woman, so she is the first NPC to switch gender twice, too.
 * One of the Oracle's phrases, "Who guards the guardsmen?", is a reference to "Quis custodiet ipsos custodes," a Latin phrase meaning "Who will guard the guards themselves?", or alternatively "Who watches the watchmen?", generally attributed to the Roman poet Juvenal.
 * In ancient times, oracles would live on top of mountains, and were consulted by the kings and leaders of countries. They were considered close to the gods (as the Oracle in RuneScape is as well).
 * One of her phrases, "When in Asgarnia, do like Asgarnians do," is a reference to the phrase "When in Rome, do as Romans do".
 * One of her phrases, "Do not fear the dragons...fear their kin," is a reference to the Dragonkin.
 * The phrase, "The great snake of Guthix guards more than she knows," most likely refers to Juna who is a snake guarding the Tears of Guthix cavern, and, unknowingly, the Stone of Jas.
 * The phrase "The god wars are over...as long as the thing they were fighting over remains hidden," may be a reference to the Stone of Jas or the Godsword.
 * The phrase "Jas has left a stone behind." is a reference to the Stone of Jas and hints to the possibility of numerous stones or similar artefacts of Jas. This piece of dialogue was added along with the Dragon Slayer rework in 2007, before While Guthix Sleeps and Meeting History.
 * After the Oracle's face update on 23 October 2012, the Oracle's movement animations were changed, which caused the Oracle's head to move away from her body. This has since been fixed.
 * After the release of the quest Fate of the Gods on 24 March 2014, she says: "Wen the cold wind blows." This is a reference to Wen, an Elder God.
 * She has a gravestone in the New Varrock graveyard which reads "The Oracle. Surely she could have foreseen that icefiend stampede?"