A few of the important prayers/Mantras worth chanting every minute of our life are as follows:-

1.Hare Rama Hare Rama Rama Rama Hare hare
Hare Krishna Hare Krishna Krishna Krishna Hare hare

2..SRI RAMA RAMA RAMETHI RAME RAAME MANORAME

SAHASRANAMA THATHTULYAM RAMANAMA VARAANANE

3.. SRIRAM JAYRAM JAYAJAY RAM

4..OM Namo Narayanaaya

5.OM Namassivaya

6.Om Namo Bagavathe Vasudevaya

There could be many more such Mantras/PRAYERS which are worthy of repeating any number of times in place of engaging our mind on purely mundane matters like Politics, Games, Entertainment etc. etc.

But what is to be borne in mind is that more than the Name it is the Object ( who alone is the subject according to Vedanta) that is to be remembered constantly. Similarly it is not mere Darshan of God at temples, meeting Holy people at their ashrams etc., that is important. We have live upto words/teachings of God in Avatars and of realized people like Ramakrishna Paramahamsa, Ramana Maharishi etc. etc. Namasmaranam is not the end of Spirituality. That is only a stepping stone.