Prayer to the Guru 
Gayatri Mantra
Prayers for Meals
Peace Mantra
Shri Mrityunjaya Mantra
Prayer to Sarasvati
Planet Mantras
Prayer to the Guru
From Guru Gita
Gurur Brahmaa gurur Vishnur
Gurur Devo maheshvaraha
Gurur saakshaat para Brahma
Tasmai shrii gurave namaha
The Guru is Brahma. The Guru is Vishnu.
The Guru is Lord Shiva.
The Guru is indeed the manifestation of the Supreme absolute.
Salutations to that glorious Guru.
Gayatri Mantra
From Rig Veda 3:62:10
Om bhuur bhuvah svaha
tat savitur-varenyam
bhargodevasya dhiimahi
dhiyo yonah pracodayaat
We meditate on the Self-effulgent Being
of seven planes, (like bhurloka, bhuvaloka, svaloka, etc.)
who provides light to the sun;
may He enlighten our intellect to reach the divine goal.
Prayers for Meals
From Bhagavad Gita 4:24
Om brahmaarpanam Brahma havir
Brahmaagnaau Brahmanaa hutam
Brahmaaiva tena gantavyam
Brahmakarmasamaadhinaa
Brahman is the offering; Brahman is the oblation.
Poured out by Brahman into the fire of Brahman,
Brahman is to be attained by him
who always sees Brahman in action.
From Bhagavad Gita 15:14
Aham vaaishvaanaro bhuutvaa
Praaninaam dehamaashritah
Praanaapaanasamaayuktah
Pacaamyannam caturvidham
Having become the digestive fire in the body of all living beings, I live.
Going outward (prana) and inward (apana),
I digest the four kinds of food.
From Bhagavad Gita 9:27
Yat karoshi yad-ashnaasi
Yaj-juhoshi dadaasi yat
Yat tapasyasi kaaunteya
Tat kurushva madarpanam
Whatever you do, whatever you eat.
Whatever you offer, whatever you give.
Whatever austerities you perform, Arjuna;
Do that as an offering to Me.
From Sannyas Gita
Hari daataa
Hari bhoktaa
Hari annam prajaapatih
Hari sarva sharireshu
Bhunkte bhojayate Harih
Hari (God) is the giver (of food).
Hari is the enjoyer.
Hari is the both the food and Prajapati (creator).
Hari is abiding in all beings.
Hari eats and allows to eat.
Peace Mantra
From Brihadaranyaka Upanishad 5:1:1
Om puurnam adah puurnam idam
Puurnaat puurnamudacyate
Puurnasya puurnamaadaaya
Puurnam evaa vachishyate
Om shaantih shaantih shaantih
That is full; this is full.
The full comes out of the full.
Taking the full from the full
the full itself remains.
Om, peace, peace, peace.
Shri Mrityunjaya Mantra
From Yajur Veda 3:60
Om tryambakam yajaamahe
Sugandhim pusti vardhanam
Urvaarukamiva bandhanaat
Mrityormuksiiya maamritaat
We worship the three-eyed One (Lord Shiva)
who is fragant and who nourishes well all beings.
As the cucumber is severed from its bondage (to the creeper).
May He liberate us from death for the sake of immortality.
Prayer to Sarasvati
Yaa kundendu tushaara haara dhavalaa yaa shubhra vastraavritaa
Yaa viinaa varadanda mandita karaa yaa shveta padmaasanaa
Yaa Brahmaacyita shankara Prabhritibhir devaih sadaa vanditaa
Saa maam paatu Sarasvati bhagavatii nih shesha jaadyaapahaa
Oh, the white delicate One, who is like a garland of dew drops on the moon;
Who wears a white garmant; who plays a viinaa with ornamental hands,
Bestowing blessings with her gestures while sitting on a white Lotus;
Who is always worshipped by Brahmaa, Vishnu, and Shiva.
May that great Goddess protect me and completely remove the ignorance and dullness from my consciousness.
"Most people chant the mantras, but do not go deep into their meanings and significance. Mere chanting or singing like a parrot will not give the required result." ~ Paramahamsa Hariharananda
May All Beings Be Peaceful
May All Beings Be Happy
May All Beings Be Safe
May All Beings Awaken To Their True Nature
May All Beings Be Free
Planet Mantras
Source: David Frawley
The following planet mantras are helpful to promote balance and protection from the affect of the planets:
Sun (Sunday) 
Om Suryaya Namah
Om Sum Suryaya Namah
Seed mantra: Om Sum or Ram
Moon (Monday)
Om Chandraya Namah
Om Cam Chandraya Namah
Seed mantra: Cham (pronounced chum)
Also useful: Om Somaya Namah
Mars (Tuesday)
Om Kujaya Namah
Om Kum Kujaya Namah
Seed mantra: Om Kum
Also useful is the mantra for fire, Om Ram (pronounced like rum, different than the solar mantra).
Mercury (Wednesday)
Om Budhaya Namah
Om Bum Budhaya Namah
Seed mantra: Om Bum (with the "u" pronounced as in "put")
Important is the seed mantra Aim, the mantra of the guru and of Sarasvati.
Jupiter (Thursday)
Om Brihaspataye Namah
Om Brm Brihaspataye Namah
Seed mantra: Om Brahm (bruhm)
Another good mantra is Shrim (shreem) - increases prosperity generally.
Venus (Friday) 
Om Shukraya Namah
Om Sum Shukraya Namah
Seed mantra: Om Shum
Saturn (Saturday)
Om Shanaye Namah
Om Sham Shanaye Namah
Seed mantra: Om Sham (pronounced shum)
The Vedic chant for peace, Om Shanti, Shanti, Shanti, is also good for Saturn.
Rahu
Om Rahave Namah
Om Ram Rahave Namah
Seed mantra: Om Ram (pronounced rahm)
The mantra for Shiva, Hum, (hoom) is also good as it destroys illusions and clears our psychic field of negative influences and suggestions, as is the Durga Mantra, Dum (doom).
Ketu
Om Ketave Namah
Om Kem Ketave Namah
Seed Mantra is Om Kem (pronounced like came)
