What are the benefits of chanting gayatri mantra, either spiritual, material, mental or physical?
Goddess Gayatri is called the mother of the Vedas. That is why one becomes qualified to read all the thousands of Vedic Mantras after being initiated into the Gayatri Mantra alone.
It has immense benefits and it is said to cleanse all sorts of sins when chanted.
Some verses from the Harita Smriti regarding the greatness of Gayatri:
When the recitation is performed, the Rakshasas, Pis'achas, and the dreadful huge serpents do not come near but fly away from a distance. (46)
Knowing the metre and the Rishi (saintly author), one should zealously recite the Mantrams. And knowing their meaning, a twice-born one should mentally recite the Gayatri, day and night. (47)
He, who daily recites the Divine Gayatri^ the highest [form of recitation] being a thousand times ; the middling, a hundred times ; and the lowest, ten times-; is not sullied by sin. (48)
Having rinsed his mouth, according to this regulation* a pure-minded Brahmana shorn of idleness, should,, with Kus'a in hands and his face directed towards the east or the north, perform the Pranayama thrice, and thereafter perform the sacrifice of the recitation of the Gayatri, the mother of the Vedas. (38 39)
[If unable to read any of these,] he should, daily, with a concentrated mind and following the prescribed rules, study the Gayatri, either near water or going into a forest. A thousand times form the highest recitation of the divine Gayatri ; a hundred times,, the middling ; and ten times, the lowest. He should daily recite the Gayatri. It is laid down that recitation must be made thrice [in a day.] The Lord [Brahma}, weighing, in a balance, the Gayatri and the Vedas [placed] the four Vedas on one [scale], and the Gayatri on the other. First reciting Om, he should then [recite] the Vyahriti (Bhur, Bhuvah, Swah). He should then attentively study the Gayatri. [One] becomes possessed of great prosperity [by the study of the Gayatri].
Further verses from the Usana Smriti:
The Brahmacharin, who, understanding its meaning daily reads the Gayatri, the mother of the Vedas, comes by the most excellent condition. (53)
Of all (Mantrams) to be recited, there is none superior to the Gayatri. It has been described, in the Smriti-S'astra* as the [means of the acquisition of the] knowledge of the Real.
One, by reciting the Gayatri, for ten thousand times, is freed from all sins.
Few more verses now from the Samvarta Smriti:
Being clad in a pure cloth, seated on the ground and on a pure spot, and self-restrained, and by performing the achamanan with a pure hand, one should begin the recitation of the Gayatri. (212)
By the recitation of the Gayatri, all the sins both of this world and of another, are dissipated in five nights. (213)
There is no purification of iniquitous deeds superior to the Gayatri. (214).
By reciting the Gayatri accompanied with Maha* Vyahritis and Pranayama, a Vipra becomes freed from all sins. (215)
Living on a restricted diet and being given to the well-being of all creatures, a Brahmacharin, by the recitation of one-hundred thousand Gayatri becomes freed from all sins. (216)
By officiating as a priest for him for whom no priestly service should be rendered, by taking boiled rice of a censurable wight, one, by reciting one thousand and eight Gayatri, becomes freed [from sins], (217)
As a snake throws off its slough, so a foremost of the twice-born, who daily studies the Gayatri, becomes freed [from his sins] in a month;
So, there are various such verses in Upanishads, Puranas and Smritis which praise the Gayatri Mantra.
Some further verses on the greatness of Gayatri taken from the PDF (Veda Mata Gayatri):
Gayatri veda janani gayatri papa nashini|
Gayatraya astu param nasti divi cheha cha pavanam ||
Shri Yogavalkya Maharishi declares that Shri Gayatri is the mother of all Vedas (in other words, the essence of all Vedas) and is the destroyer of all sins; there is nothing beyond Shri Gayatri in both Bhu loka and Deva loka
A similar verse from the Kurma Purana is also quoted:
Gayatri veda janani gayatri loka pavani |
Na gayatryam param japyam etat vijyanam uchayate ||
The above sloka from Kurma Puranam, while emphasizing that Shri Gayatri Devi is the mother of all Vedas, declares beyond doubt that Shri Gayatri purifies and sanctifies the Universe and there is no other Mantra that is beyond Gaytri Mantram and it indeed is Vigyanam.