All Yoga types may decrease or eliminate depression as well as stress, anxiety and physical problems. The benefits are too numerous to even mention. All of the various branches of yoga can be practiced exclusively, yet they are all related, and perfectly complimentary to one another.
A NOTE OF CAUTION:
It is very important, especially for anyone suffering from severe depression, bipolar disorder or any other mental illness, to seek the guidance of a trained, experienced teacher before embarking on any Yoga types that involves meditation, breath control or other practice that quickly impacts one's state of consciousness. Anyone with a tendency towards suicidal thoughts or psychosis may experience a worsening of these symptoms with certain yoga practices.
Hatha Yoga: Involves both pranayama (breathing techniques for life-force control) and asanas (physical postures) which are quite vigorous, and have tremendous benefits physically, as well as emotionally and spiritually. As in all Yoga pathways, the goal is not physical fitness, but rather strengthening and balancing the nervous system in order to capacitate super-conscious states of awareness and energy.
Kundalini Yoga: Not a truly traditional yoga but a modern day creation which has been widely marketed and popularized. Kundalini is a well known component of yoga philosophy and is known to all yogic meditation traditions. A comprehensive system with a focus on opening the pranic or psychic energy centers within the spine, called chakras. This ultimately awakens the Kundalini energy, which normally lies dormant at the base of the spine. When aroused, the potential energy becomes a consciousness-altering force, and rises through each chakra, resulting in states of super-consciousness, and bliss.
Jnana Yoga: The path of Self-knowledge. Well suited for those who are intellectually inclined, have excellent concentration and strong will and a relentless thirst for the Truth. This path involves the giving up of all paths and techniques to realize that the Self exists in it's pure state here and now. Often referred to as Advaita (non-duality). This path may involve Insight Meditation but there are no prerequisites, only the question: "Who am I." Influential teachers of this path have been Ramana Maharshi, and Swami Vivekananda, who was the first Indian teacher to teach to wide audiences in America.
Bhakti Yoga: Bhakti means devotion. This is an emotional path of total surrender, love and dedication to one's chosen image of God, be it Jesus, Krishna, or any other divine figure. Self-less action is practiced for the good of humanity and to humble oneself. Bhakti is a major element of most religions. This path is often practiced in conjunction with other types of Yoga.
Karma Yoga: The path of Self-less action. Total devotion to one's work in the world with no expectation of reward. Absorption in the object of activity with gratitude, love and compassion. As in Bhakti, all actions and their rewards are given to the divine. This path is also usually combined with other Yoga types. Mother Therese, and Gandhi are great examples of this type of path.
Yoga Nidra: Yogic Sleep. In the Yoga of deep conscious sleep, you remain awake as your body goes into a deep sleep state, beyond the restless dreaming state.
Tantra Yoga: Perhaps one of the the most mysterious and misunderstood Yoga types. Tantra is often mistakenly associated with new age sexual tantra practices. This is a school of Yoga which is very old and which incorporates many elements of other Yogic practices, as well as ritual. There is much focus on integrating the shadow aspects of the ego, as well as the union and balance of one's feminine and masculine energies to achieve wholeness, ultimately transcending all desires and illusions. Tibetan Buddhism has been closely associated with this path.
Kriya Yoga : Lost to the mainstream world during the Middle Ages, this ancient path was revived again in the 1800's by the ageless sage Trambaknath (known as "Babaji" in the book Autobiography of a Yogi). Originally rooted in the ancient Nath sect of Himalayan Yogis and passed down through successive teachers to Paramahansa Yoga, one of the most influential international teachers in recent history. Yogananda brought these teachings to the West and was at the height of his activity in America in the 1920's and 30's. This path is practiced by all types of people, but is known to be well suited for the demands of a life in the world. Some of the most influential teachers of this path have been married, had children and jobs, while attaining staggering heights of Self-Realization. Yogananda called it "the airplane path," because of it's ability to rapidly accelerate one's consciousness evolution. Kriya Yoga primarily involves pranayama (control of life energy through breath), and meditation.
Surya Yoga : Solar Yoga uses the healing energy of the sun to cleanse, rejuvenate and heal the body and mind. Such practices are diverse and exist in many cultures. Surya Namaskar is one of the most widely practiced techniques and is taught by many teachers in the west. Surya Yoga or Solar Yoga are specific traditional practices that should not be confused with casual "sun gazing" methods. Surya Yoga may only be taught through face to face instruction. Traditional techniques of solar yoga exist among the Himalayan yogic traditions including Kriya Yoga.
Laughter Yoga: I hesitated to include this among the timeless traditional yoga types listed above. These techniques of self-induced laughter - usually with a group of people - were developed by Dr. Medan Kataria in the 1990's. It has become a wildly popular world-wide phenomenon, and also gained the attention and respect of many researchers and medical professionals for its many health benefits. Because the benefits are undeniable, I felt it should be included here.