Why do Hindu gods have many arms?

^^ lol

I always thought they were the patron gods of Paperhangers.

Wasn't there another Hindu god who had the head of a rooster?

Another animal-headed god was Varaha the boar, an incarnation of Vishnu. He saved the world from drowning by balancing it on his tusks

Oh where to start? These are all ancient manifestations of the divine. The animal forms are most ancient going back to a shamanistic time with a world inhabited by divine animal spirits which adepts would try to tap into when going into a trance. The many arms is as already been described, the ability of the deity to do many things and be in many places at once. The blue colour is most interesting, and I came across this when looking at Sumerian art. Some pieces use lapis lazuli in figures looking to the heavens. It was considered to have divine properties, lapis lazuli, and would have been seen this way over vast distances. Lapis Lazuli at the time, and still is now, was mined in Afghanistan, which is some distance even now.    

Hindu gods like Ganesh, Brahma and Varaha often have many arms. Some have animal heads. Why are they depicted this way?

Dear Nick the Gods with many arms is not that tghose Gods existed in such a way and nor its a person of any kind as some people in above likes to make joke of. Aside from joke what you need to do is study Hindu symbolism. Although you asked a great question but the fact people in here might not be informed enough to give such explainations. BTW Ganesh, Brahma and Varaha are mostly south Indian Gods which is believed to be same as Shiva, Krishna and etc. Example of such symbolism includes the power they hold over people, over the planet or sometimes the Arms, magic and weapons they posses. 

Maybe you guys are looking too far into this. Maybe the colour doesn't have any historical explanation. Maybe it symbolizes something relating solely to the colour, same as red is symbolyses love and purple royalty. Blue is usually considered to represent calmness and serenity which are important concepts in eastern religions.

Color revive statue and make it beautiful.As we have seen color also gives character and role of God in their
lives! 

Osiris was green to show that he was dead. But of course his death and revival was also linked to the agricultural cult.