Mantras from Vedas and Upanishads:

Shanti Mantras:

• Om Asato Ma Sadgamaya
  ॐ   असतो   मा   सद्गमय
  (Lead us from Unreal to Reality, Lead us from Darkness to Light)
  
  See also Om Asato Ma Sadgamaya - line by line
• Om Bhadram Karnebhih Shrnuyama Devah
  - from Mundaka Upanishad, Mandukya Upanishad, Prasna Upanishad
  ॐ भद्रं कर्णेभिः शृणुयाम देवाः
  (May we Hear what is Auspicious, May we see what is Auspicious)
• Om Dyauha Shantirantariksha Shantihi
  ॐ   द्यौः   शान्तिरन्तरिक्षं   शान्तिः
  (May there be Peace in Heaven, Sky, Earth, Water, Plants, Trees; May there be Peace in All)
• Om Purnamadah Purnamidam
  - from Brihadaranyaka Upanishad, Ishavasya Upanishad
  ॐ   पूर्णमदः   पूर्णमिदं
  (That is Full, This is Full, From Fullness comes that Fullness)
• Om Sahana Vavatu
  - from Taittiriya Upanishad, Katha Upanishad, Mandukya Upanishad, Shvetashvatara Upanishad
  ॐ   सह   नाववतु
  (May God protect us, May God nourish us, May we work together and let our study be enlightening)
• Om Sarve Bhavantu Sukhinah
  ॐ   सर्वे   भवन्तु   सुखिनः
  (May all be Happy, free from Illness, see what is Auspicious and may no one Suffer)
• Om Sarvesham Swastirvavatu
  ॐ   सर्वेशां   स्वस्तिर्भवतु
  (May there be Auspiciousness, Peace, Fullness and Prosperity to All)
• Om Shamno Mitrah Sham Varunah
  - from Taittiriya Upanishad
  ॐ   शं   नो   मित्रः   शं   वरुणः
  (May the presiding deities be propitious to us, Adoration to Brahman, May Brahman protect us)
• Om Vang Me Manasi Pratisthita
  - from Aitareya Upanishad
  ॐ   वाङ्   मे   मनसि   प्रतिष्ठिता
  (May my mind be fixed in my speech, May Atman manifest unto me, and reveal unto me the Highest Knowledge)

Vedic Suktams:

• Apah Suktam
  - from Rig Veda 10.9
  आपः   सुक्तम्
  (O Water, because of your presence the atmosphere is so refreshing; with the auspicious sap of yours provide nutrition to our crops, with the medicinal herbs protect our body and with your Agni fill our body with lustre.)
• Kshetrapati Suktam
  - from Rig Veda 4.57
  क्षेत्रपति   सुक्तम्
  (O Lord of the Kshetra [Field], with the sweet waves of Mother Nature's blessings, may you milk our Fields like the Milk of a Cow and yield abundant harvest)
• Purusha Suktam
  - from Rig Veda 10.90
  पुरुष   सुक्तम्
  (The Purusha, the Universal Being with thousand heads, thousand eyes and thousand feet, pervades the creation and transcends it)