As you probabily already know, Saiyuki is based on the popular Chinese legend "Hsi Yu Chi" (=Journey to the west), although the Saiyuki charachters are very, very different from the originals^^**
--> The legend
The original legend begins with the born of the Monkey King Son Wukong, born from the earth as a stone egg. In a way I don't know (sorry! but I think there is a god involved) he's transformed into an ordinary monkey. He lives peacefully as the king of the monkeys on the Mountain of Flowers and Fruit, until one day, after the death of one of the oldest monkey, he realizes he will die too, so he decides to obtain immortality. After having wandered around, he meets an immortal patriach who accepts to teach him the secrets of long life (at first Monkey was tossed out**). So Monkey is locked in a room to learn. After some years, he finally exits, with the power of flying, of transform himself into anything he wants and so on. He also has a new weapon stolen from an underwater kingdom: a staff which can grow longer or shorter according to his will. Monkey keeps it behind his ear (miniaturized, obviously!).
He comes back to the Mountain, and the first thing he does is teaching to the other monkeys how to fight; then he causes a mess in Underworld, making sure no monkey of the mountain can die, and annoys the Dragon king of the Eastern Ocean. So the officials of Heaven decide to give him a job in Heaven in order to keep an eye on him. Monkey at first is happy, but soon he discovers why he was invited there, and also that the work he's been given is a low-ranking work. He gets veeery angry, leaves his place and steals and eats the sacred peaches which give immortality. Then he tries to conquer Heaven, but he loses.**
It is decided Monkey has to be executed... but now he's immortal! So Buddha intervenes challenging him to a race. Monkey accepts and in a moment he travels lots and lots of miles, reaching the end of Heaven... just to find himself on Buddha's hand!! He's lost again and he's chained under the 5-elements mountain, with the order to remain there until a monk will come to free him. When this will happen, he will have to escort him in his journey.
After years of waiting, finally the monk Tripitaka arrives. Tripitaka is a Chinese priest who has been sent by Heaven towards India, to retake some sacred sutras. After having done this, he will be allowed to enter Heaven. Anyway, Tripitaka frees Monkey and starts travelling with him... But Monkey isn't so happy of this and plans an escape. So the monk (warned by Buddha) manages to put a diadem on Monkey's head, which can grow tighter if Tripitaka chants a particular prayer... so Monkey calms himself and rebels no more against the monk.
Well, now the second and most famous part of the story begins...
Tripitaka and his 3 companions travel towards west, and face any sort of dangers: youkais (=demons... mostly female spider demons**), dragons, monsters and so on. They are attacked lots of time because all the demons want to eat the monk.** Their journey takes nearly 20 years (*O_o*) and has a happy ending.* (I'm not sure, but I think both Tripitaka and Monkey are allowed to enter Heaven, while the other 2 travellers become the keepers of the Heaven gate, deciding who is worth to enter or not.)
Tripitaka is the typical monk... gentle and naive, he can't fight and lets his 3 companions to do all the work.
About Son Wukong read what I've written before.^^;***
The other 2 demons in the journey are Chu Pa Chieh and Sha Monk.
Chu Pa Chieh was a general in the Heaven army, but he fell in love with the moon goddess. The gods aren't allwed to marry other gods, so he was punished with reincarnation. With a very unlucky, he fell in the place where the humans who must be reborn as animals are gathered... so he reincarnates in a pig.^^* He is often hungry, and likes enjoying the life drinking, eating meat and sleeping with women.**
Sha Monk is very calm and silent, he doesn't talk much. (*Seems Gojyo changed role with Hakkai.***) In Heaven he was a cupbearer, but he accidently broke the emperor's favourite cup, so as punishment he was assigned to guard a river (O_o only for a cup????). He passed so much time in the river that he became a river demon.
--> A true story?
Actually, in about 600 AD, a Chinese monk named Hsuan Tsang left from his temple Changan heading towards India. The purpose was to collect some buddhist scriptures and take them to China so the people could learn about the religion. Returned home, he became a favourite of the Emperor and was given the honorific name "Tripitaka". So all sort of stories began to be told about his journey, and someone introduced the monkey... who in short time became so popular that he took the role of protagonist.**