Goku Himself: He's an annoying little brat on out set, though his love and his devotion to Sanzo is very strong and endearing. After being locked under a mountain for about 500 years (not revealed in the manga why yet) for some miss deed in his time in Heaven (read the 'Saiyuki Gaiden' for this part of his history), Sanzo came and released him. He's bouncy and as all kids seems to want to know the "why?" of everything, he's a little naive but he has been out of it for a long time. He is basically the "Monkey King" in this strange 'Journey to the West' tale, with his extending staff for a weapon. The crown he wears around his head is his 'Demon Inhibiter' and stops him turning into the mad longhaired demon that he is.
He's got a bottomless stomach, and it's his top most whine, Sanzo once comments that Goku is just making up on 500 years of not eating, and he doubts he could starve even if he tried.
He also has no memory of his time in heaven, which is probably a good thing, but explains why he's so attached to Sanzo. (of which is hinted at in Manga & Anime cannon)

Goku's Relationship with the Others:
With Sanzo = His loyalty to Sanzo is unquestionable, maybe cos Sanzo released him from his prison and proceeded to look after him, with some help from his lost memories from when he was in heaven. Their relationship is more like son and reluctant father, but it seems to work.

 
With Hakkai = Goku respects Hakkai, but their relationship is a casual one.

 
With Gojyo = They have an interesting brotherly relationship, mostly fighting all the time and calling each other names, ^_^