The most common mantra is the maha mantra:
hare krishna hare krishna krishna krishna hare hare
hare rama hare rama rama rama hare hare
Some scriptures have the mantra reversed beginning first with hare rama.
This is a nama mantra which does not require initiation by a guru, and can be chanted by anyone at anytime.
The Kali Santarana Upanishad states about this mantra:
iti shodasakam namnam
kali-kalmasha-nasanam
natah parataropayah
sarva-vedeshu drisyate
"The sixteen words 'Hare Krishna Hare Krishna Krishna Krishna Hare Hare Hare Rama Hare Rama Rama Rama Hare Hare' are especially meant for completely destroying all the contamination of Kali yuga. To save oneself from the contamination of Kali Yuga, there is no alternative in all the Vedas except the chanting of this sixteen-word mantra."
Other common mantras for Lord Vishnu are om namo bhagavate vasudevaya and om namo narayanaya.