Ganesh is the elephant-god and owes his unusual form to his father, Shiva. Dad returned home after a few thousand years of meditation (and he only went out for some cigarettes) to find his wife, Parvati, with another man. He promptly cut the intruder’s head off before he was reminded that it was his son. Full of remorse but still blood-thirsty he cut off the head of a passing elephant and stuck it on.
Ganesh is also hugely popular and is regarded as the god of good fortune. With his long trunk he lifts your problems out of the way. By accepting such a funny-looking god is also a way of embracing the divine nature that lies behind all things. i.e. Believe that and you can believe anything.
Ganesh is one smart god too. He won the right to be lord of humanity over his brother, Kartikey. They had a race to run around the universe; so off Kartikey went at top speed while Ganesh simple walked around his parents, Shiva and Parvati – the implication was that all the universe was contained therein