While Hare Krishnas may be one of the best known branches of Hinduism, just because you're aware of them doesn't mean that you're familiar with any actual Hare Krishna beliefs. While they have some things in common with Hinduism and other Indian religions, the Hare Krishnas remain their own distinct group with a very different set of beliefs from those you may be familiar with in the West.
Formally known as the International Society for Krishna Consciousness (ISKON) and nicknamed Hare Krishna because of their famous chanting, it was established in New York City in 1966 by A. C. Bhaktivedanta Swami Prabhupada - though it is rooted in the Gaudiya Vaishnava tradition which extends back to the 15th century in India and the beliefs of Sri Chaitanya of Bengal. While Hare Krishna is probably best known for its chanting and promotion of vegetarianism, there is a much more complex belief system at play. They draw from the Bhagavad Gītā and the Bhagavata Purana as their sacred texts and seek to cultivate spirituality through the word of Krishna, but that's just the beginning.
While in some religions "God" remains a faceless omnipresence, Hare Krishnas believe that their God, Krishna, is a person. This is the case, in part, because they find evidence for this in their sacred texts. However it also follows a certain logic - if everything else in the world has a physical form, they believe that the creator of that must also:
"However, there is overwhelming evidence suggesting that the Supreme Person is not abstract at all. In the Vedas - the oldest and most comprehensive of all world scriptures - one can discover that the Absolute Truth has both impersonal and personal aspects... Since everything in our experience has form and qualities, it makes sense that the source of all sources should also, to an infinite degree. As drops of ocean water have the ocean’s qualities in minute degree, our forms and personalities are infinitesimal samples of the infinite Supreme Person."
Hare Krishnas believe that we are not individual bodies but instead are all part of a spiritual whole. Each person is a soul, a part of Krishna.
"We are not our bodies but eternal, spirit souls, parts and parcels of God (Krishna). As such, we are all brothers, and Krishna is ultimately our common father. We accept the process of transmigration of the soul (reincarnation)."
In addition, the Bhagavad-Gita mentions reincarnation explicitly as "the embodied soul continuously passes, in this body, from boyhood to youth, and then to old age, the soul similarly passes into another body at death. A sober person is not bewildered by such a change.” So the idea is that your soul, or the part and parcel of Krishna's soul that you are, has lived many lifetimes before; you just don't remember them. But for Hare Krishnas, the fact that you have no memory doesn't mean that it didn't happen.
In Hare Krishna, yoga is essential, but it's not the yoga you are probably be thinking of. Although the Bhagavad Gita, the main spiritual text for Hare Krishnas, mentions many physical yogas that you're probably familiar with, it goes a step further. The importance of bhakti-yoga ("the path of dedication and love") is a much more holistic yoga "practice" than going to a studio and doing a flow class twice a week. In fact, it's a key belief of Hare Krishnas. As explained in the ISKON website, "physical exercises are just one step on path of God realization. The Gita ultimately prescribes bhakti-yoga... as the culmination of other yoga practices. Bhakti-yoga focuses on developing our dedication, service and love for the Divinity, Lord Krishna."
Not only does this including chanting and meditation, but it also extends to the consumption of sanctified food and "living in a way that upholds the principles of truthfulness, mercy, austerity, and cleanliness."
Hare Krishnas are strict vegetarians who also avoid eggs. This is because they believe that cooking is a sacred experience and "should be based on principles of compassion, non-violence and balanced living." Not only is killing animals thought to be violent and bad for your consciousness, but all animals are also Krishna's creatures with souls of their own, so killing them would be disrespectful and an affront to Krishna.
And Hare Krishnas pay their vegetarianism forward. There have been cook books, Hare Krishna restaurants, and the world’s largest free vegetarian food relief program all from devotees and ISKON.