Mahaa Mrityunjaya Mantra
Om trayambakam yajaamahe, sugandhim pushtivardhanam
Urvaarukam iva bandhanaat, mrityormukshiya maamritaat
Om Shaantih Shaantih Shaantih

Oh three-eyed Lord Shiva, I meditate upon Thee. You whose body has a fragrant odor, who enriches our nourishment, like a creeper which is released from its branch when ripe, please release me from death and human limitation and grant me immortality.

Maha Mantra
Hare Raama Hare Raama, Raama Raama Hare, Hare;
Hare Krishna Hare Krishna, Krishna Krishna Hare Hare.

Love and adorations to Lord Raama and Lord Krishna.

Guru Stotra
Gurur Brahmaa Gurur Vishnuh, Gururdevo Maheshvara;
Guruh Sakshaat Param Brahma, Tasmai Shree Gurave Namah.

Guru is Brahmaa, Guru is Vishnu, Guru is Maheshvara (Shiva), Guru is Param Brahma (Transcendental God). To such a Guru, I offer my prostrations.

Dhyana Mulam Gurur Murti, Pooja Mulam Gurur Padam;
Mantra Mulam Gurur Vakyam, Moksha Mulam Gurur Kripa.

Guru's image is fit to be meditated upon, his feet is fit to be worshipped;
His words are like mantras, his grace is equivalent to moksha.

Deity Mantras

Vedantic or Moksha Mantras
Om, So-Ham, Shivo-ham, Aham Brahmaasmi, Tat Tvam Asi, Hari OmTat Sat 

Tantric Mantras
Om Aim Hreem Kleem Chaamundaai Vicche.
Om Hreem, Om Shreem, Om Kleem, etc.