According to the Cochrane collaboration:
Yoga is successful, short term, for Carpal Tunnel Syndrome:
Current evidence shows significant short-term benefit from oral steroids, splinting, ultrasound, yoga and carpal bone mobilisation.
This is in line with more general findings that there pain reduction can be induced via meditation.
Yoga is better than regular exercise for schizophrenia patients, but not better than standard or non standard care
One trial compared exercise with yoga and found that yoga had a better outcome for mental state.
—source 1 source 2 source 3
However, yoga had merely "potentially beneficial effects" on depression:
Overall, the initial indications are of potentially beneficial effects of yoga interventions on depressive disorders. Variation in interventions, severity and reporting of trial methodology suggests that the findings must be interpreted with caution.
Yoga is just as effective as other relaxation/meditation techniques:
Yoga did not show significant effectiveness in treating obsessive-compulsive disorders compared with Relaxation/Meditation.
Finally, yoga is not demonstrably effective on epilepsy:
No reliable conclusions can be drawn regarding the efficacy of yoga as a treatment for epilepsy.