Shri Ganesha Gayathri Mantra

Lord Ganesha

The Ganesha Gayathri Mantra addressing Lord Ganesha to remove all obstacles and to succeed in all endeavours. It is very important to chant the Mantra correctly. Each syllable of the Mantra is referred to as a Beeja, a sound-seed that represents energy, and the Beejas form the building blocks of the Mantra itself. The Gayatri Mantras contain a sequence of 24 Beejas, 3 lines of 8 Beejas each. Every Gayatri Mantra has an associated rishi, chandas and devata (God it addresses).

The most popular of the Gayatri Mantras is the one that addresses the transcendental divinity, the giver of all energy, light and the life force itself (sometimes said to the the Sun). This Mantra is considered be amongst the highest and most powerful of all the Mantras and is also sometimes referred to as the Ved Maata (Mother of all Vedas). 

ॐ एकदन्ताय विद्महे

वक्रतुण्डाय धीमहि।

तन्नो दन्ति प्रचोदयात्॥

Om ekadantAya vidmahe

vakratUnDAya dhImahi |

tanno danti pracodayAt ||

ॐ - the Pravana Mantra, referring to the all-pervading divinity in this universe. This Beeja Mantra is an extensive topic in itself and it is impossible to even begin explaining it here. More importantly, I am in no way qualified to do so, but I will during some other post point to some very interesting resources that will shed more light on the topic.
विद्महे - praise/worship of the Lord
धीमहि - meditate upon
तन्नो  - One who is to us
दन्ति - the tusked One
प्रचोदयात् - impel us forward towards realization

I worship You, O’ single-tusked Lord, One with a twisted trunk. I meditate upon You, the tusked One, to impel me towards awakening my consciousness and realizing my Self.
The other variations of Ganesha Gayatri are the following:

ॐ तद्पुरुशाय विद्महे

वक्रतुण्डाय धीमहि।

तन्नो दन्ति प्रचोदयात्॥

Om tadpurushAya vidmahe

vakratuNDAya dhImahi |

tanno danti pracodayAt ||

ॐ लम्बोदराय विद्महे

महोदराय धीमहि।

तन्नो दन्ति प्रचोदयात्॥

Om lambodarAya vidmahe

mahodarAya dhImahi |

tanno danti pracodayAt ||

All 3 versions stay true to the objective of the Mantra itself, differing only in their praise for Lord Ganesha’s attributes.