(This post does not induce religion or encourage Hinduism in any sense. It is only my view of why Hindu deities have many heads and hands.)
This led to the belief that a Hindu deity is multi-headed and "spider" handed, sort of. In fact, I find many Hindus refer to God as someone with the same physical description.
This is what I think:
In a picture, personality traits / characters are depicted via a face. So a gentle character has a gentle face, an angry character has a red face, a frightening character is depicted as someone who has gorging eyes and probably a tongue coming out of mouth. When an artist wants to show the various traits/characters (read "faces") of a Hindu god/goddess, there is a dilemma. A single face won't be able to cover all the traits. Hence, the artists chose to give the god/goddess the many heads - in fact many faces.
Hands denote ability. Even in English language, the use of the word "ambidextrous" is used to denote skill of the person and not just "someone who can use both hands with equal skill". To show that a person is skillful at sword fight, a sword is painted in his hand. Thus, to denote many abilities, the artist drew many hands, each depicting a particular skill.
Thus a Hindu deity is shown having many heads and many hands.
(This explanation is entirely my own and I find this quite logical. If someone else has said the same thing, I haven't read it.)