There are 6 main branches of yoga:
Raja Yoga – the yoga of meditation
Jnana Yoga – the yoga of wisdom
Bhakti Yoga – the yoga of devotion
Karma Yoga – the yoga of service
*Tantra Yoga – the yoga of sacred ritual
**Hatha Yoga – the yoga of physical processes
More commonly in the west we associate yoga practice with the branch of Hatha Yoga, which incorporates pranayama (breath work), asanas (postures), meditation.
This leads to the 8 limbs of yoga (ashtanga).
Including: Ahimsa (non violence), Satya (truthfulness), Asteya (non-stealing), Brahmacharya (control of the senses), Aparigraha (non-covetousness).
Including: Saucha (cleanliness), Samtosa (contentment), Tapas (heat; spiritual austerities), Svadhyaya (self-study, study of sacred scriptures), Isvara Pranidhana (surrender to god).
The postures practiced in a yoga class
Control of prana (life force) or breath control or conscious lengthening of the breath
Withdrawal of the senses
Single point of focus or concentration
Meditation or contemplation
A state of ecstasy or oneness
It is said that the 8 limbs of yoga are a progressive series of steps or disciplines which purify the body and mind, ultimately leading the yogi to enlightenment.
*Note: Kundalini yoga belongs to the tantra tradition
**Note: the branches of yoga can change slightly from definition to definition and Hatha Yoga can be considered a part of Raja Yoga.