There are tens of thousands of Mantra in Ved, including Sookt and Mahaa Vaakya etc. Many of these Mantra, or Sookt are very famous and popular and people recite them everyday, but there are three Mantra which are most popular among people and are very effective too.
(1) Gayatri Mantra
The first Mantra is Gayatri Mantra. Gayatri Mantra is the most important Vaidik Mantra and especially now-a-days is very popular. Many Gayatri Dhaam have developed at many places to spread the greatness of Gayatri Mantra and they inspire people to recite it all the time. They have removed all the limitations also from Gayatri Mantra recitation. which Rishi placed before - such as women cannot recite Gayatri Mantra, or one needs initiation to recite Gayatri Mantra etc etc.
Gayatri Mantra is a Ved Mantra and it appears in three out of four Ved, four times, although in different versions
(1) Rig Ved, 3.62.10 - begins with "Tat Savitur Varenyam ..."
(2) Yajur ved, 22.9 - begins with "Om Bhoor Bhuvah Swah ..."
(3) Yajur Ved, 36.3 - begins with "Bhoor Bhuvah Swah ...."
(4) Saam Ved, 13.1462 - begins with "Tat Savitur Varenyam ...."
The full Gayatri Mantra runs like this --
Om Bhoor Bhuvah Swah, Tat Svitur Varenyam, Bhargo Devasya Dheemahi Dhi Yonah Prachodayaat
Which means --
Om Bhoor Bhuvah Swah - are the three Vyaahriti
Tat Savitur Varenyam - That splendid magnificence of Savitri is assuredly Savitri, the inspirer, the life giver, the stimulative force.
Bhargo Devasya Dheemahi - May we meditate on the life giving Divinity Savitri
Dhiyo Yonah Prachodayaat - May he himself illumine our intelligence. May he himself breath into us.
From its meaning, it seems that it is the prayer to Soorya Dev to obtain Gyaan (knowledge). Read in details at Gayatri Siddh Peeth site.
(2) Panchaaksharee Mantra
Panchaaksharee Mantra is "Namah Shivaaya". This Mantra is also a Vaidik Mantra, and is most popular among Shaivaites. It is supposed to be the best Mantra among 7 Crores of Mantra. This Mantra comes in Namakam Chamakam, or Shree Rudram, or Rudram Chamakam. Namakam Chamakam is one of the five scriptural texts chosen by the ancients for constantly repetition and meditation. These words are the part of the Vaidk Stotra from Shukla (white) Yajur Ved, Taitteerya Sanhitaa, 188.8.131.52. Ved says that who does Jaap of this Mantra becomes free from the cycle of births and deaths.
(3) Mahaa Mrityunjaya Mantra or Mrit Sanjeevanee Mantra
The third powerful Mantra is Mahaa Mrityunjaya Mantra. This Mantra is also for Shiv. It is related to Shukraachaarya Jee and Maarkandeya Rishi. It is the same Mantra by which Shukraachaarya Jee used to bring dead Asur alive after they were dead in Devaasur Sangraam. When Devtaa noted this they requested their Guru Brihaspati Jee to learn that mantra so that he could also bring them alive after they were dead. So he sent his son Kach to Shukraachaarya Jee to learn this knowledge. He learnt that knowledge and with that knowledge Devtaa could be brought to life after they were dead.
This Mantra is a part of Rudra Ashtaadhyaayee, and in its parent Ved, Shukla and Krishn Yajur Ved. Both the Mantra are similar with the exception of one or two syllables. Both these Mantra run like this --
(1) Rig Ved, 7.59
Om Tryambakam Yajaamahe Sugandhim Pushti Vardhanam
Urvaa Rukamiva Bandhanaan mrityor Muksheeya Maamritaat
It alleviates even the most deadly disease and death
(2) Shukla Yajur ved, 3.60
Om Tryambakam Yajaamahe Sugandhim Pati Vedanam
Urvaa Rukmiva Bandhan Adito Muksheeya Maamutah
This the prayer of a bride for her husband
All the three Mantra have their own importance in their aims, have their own place in the society and have their own place among their Bhakt.