This is one of my favorite mantras (Vedic Verses)  to recite.

Sarve bhavantu sukhinaH
Sarve santu niraamayaH
Sarve bhadraani pashyantu
maa kash-chid dukh bhaag bhavet
Aum Shaanti Shaanti Shaanti Aum

Meaning

May all be happy.
May all enjoy health and freedom from disease.
May all have prosperity and good luck.
May none suffer or fall on evil days.

This mantra is for Peace invocation.  It is intended to be recited for the welfare of humanity as a whole.  The reason it is one of my favorite mantras in Hinduism is simple — the mantra is the most selfless prayer ever.   You are not asking anything for you by reciting this, but rather the goodwill and welfare of everybody in the world is being prayed for.  In my humble opinion, it is a representation of Hinduism, a non-violent, peaceful religion.

Here’s the mantra (verse) in Sanskrit:

ॐ सर्वे भवन्तु सुखिनः सर्वे सन्तु निरामयः।
सर्वे भद्रणिपश्यन्तु मा कश्चिद्दुःख भाग भवेत्॥

(mantra taken from Brihadaaranyaka Upanishad 1.4.14)