Lord Ganesha is the elephant-headed God. He is worshipped first in every Hindu prayer. His Names are chanted first before any auspicious work is begun, before any kind of worship is begun.
"OUM SHREE GANESHAYA NAMAH"
"ओउम श्री गणेशाय नमः"
This chant is very powerfull chants in Hindu dharama. This mantra is chanted before starting any auspicious work with a beleif that Lord Ganesha would be there to remove all the obstacles that will come accross in completion the task we are going to begin.
"वक्रतुंडा महाकाय सूर्यकोटि समप्रभा निर्विघ्नं कुर्मे देव सर्वकर्येशु सर्वदा "
There is a very interesting story behind this that why Hindu's worship first Lord Ganesha.
The Story :
Once Lord Ganesha and his elder brother Lord Kartikeya decided to have a race. They went to their parents ( Lord Shiva and Godess Parvati). Lord Shiva said go and take a round of entire world and come back to us. Whoever will come first would be worshiped first before any worship starts.
The race began and Lord Kartikeya started the race but not Lord Ganesha.
Lord Ganesha just took a round of Lord Shiva and Goddess Parvati.
After Some time Lord Kartikeya returned back and he saw Lord ganesha has already reached at the point from where the race has started.
He asked Lord ganesh how come you can take a round of earth and sky so fast.Lord Ganesha replied that I have took a round of Lord Shiva and Goddess Parvati and I am done.Lord Kartikeya asked again but the race was took a round of earch and sky not the father and mother.
Lord Ganesh replied polietly that When I took the round of Father(Lord Shiva) I completed the round of sky as Father is a simle of sky and when I took another round around Mother(Goddess Parvati) I completed the round of earth as Mother is the symble of earth.
So I am Done.
After listening this answer all the Gods and Goddess present there started chearing up Lord Ganesha.
Since then Lord Ganesha is being wrshipped before any other Gos is worshiped.
-- Jai Ganesha.