Sanskrit mantras are very potent sounds. The effect they produce will depend on the correct pronunciation. If they are not pronounced properly they will have a contrary effect.
Mahamrityunjaya Mantra for Shiva
This is for maintaining good health.
ॐ त्र्यमब्कं यजामहे सुगिन्धं पिुष्टवधनर्म्
उवारुर्किमव बनध्नान्
मृत्योमुर्क्षीय मामृतात ।
oṃ tryámbakaṃ yajāmahe sugandhíṃ puṣṭi-vardhánam,
urvārukam íva bandhánān mṛtyor mukṣīya mā 'mṛtā́t.
I worship the fragrant, three-eyed one (Shiva) in order to get perfect health and to release me from the coils of mortality as effortlessly as a ripe cucumber falling from its stalk and grant me immortality.
Surya Gayatri Mantra
This should be repeated as many times as possible in the morning when the sun is rising, at noon when it is at its zenith and in the evening when it is setting. Very good for increasing memory and all round well-being.
ॐ भूभुवर्: स्व:
ॐ तित्सिवतुवर्रेणयं
भगोर्देवस्यधीमिह
धियोयोनं: प्रचोदयात।
Oṃ bhūr bhuvaḥ svaḥ
Tat savitur vareṇyaṃ
Bhargo devasya dhīmahi
Dhiyo yo naḥ prachodayāt.
We meditate on the light of the luminous God Savitur, who is well-known in the Vedas, who is the inspirer of all beings, the inner Self, who is the creator of the universe. We mediate on that adorable light which is the Self of the Supreme Lord of the universe, adored by all as the sole object of worship. It is the giver of knowledge and destroyer of ignorance. It is the light of the Supreme Brahman itself.
Gayatri Mantra is said to be the quintessence of the Vedas. It gives us the knowledge of the oneness of the jivatma (embodied soul) with the Paramatma (cosmic soul). The sun is said to be the “pratyaksha devata” - the God that you can see with your eyes, so the stotra (hymn) is addressed through the sun to that supreme Brahman.
“Bhur, bhuvah, swaha!” stand for the three worlds, earth, heaven and the interim space.
It also stands for existence (bhur), consciousness (bhuvah), and bliss (swaha).
Vanamali Mantra
This can be said whenever we are in a dangerous situation. It must always be said when you leave on a journey and also when you go to sleep. It is a “kavacha” or armour made of the names of Krishna.
वनमालीगदिशारंगी शंकिचक्रीचनंदकी
श्रीमननारायणेविष्णु: वासुदेवोभिरक्षतु ।
Vanamālī gadī śārṅgī śaṅkhī cakrī ca nandakī,
śrīmān nārāyaṇō viṣṇurvāsudevōbhirakṣatu.
O Vishnu who wears the wild flower garland and carries the mace, bow, conch, chakra and sword, may you protect me from all sides.