Humans can suffer from a broad variety of mental health problems - from mood disorders like depression and Bipolar disorder, to anxiety and personality disorders, and dissociative and psychotic conditions like schizophrenia. It's estimated that about 20% of the human population experiences some form of mental illness.
Because we can't know what dogs are thinking, we aren't completely sure what range of mental health issues canines experience, but it appears that most of the emotional and cognitive problems experienced by dogs typically fall under the spectrum of anxiety.
The age-old debate of whether canine (and human) mental health is influenced more by "nature" or by "nurture" is far from settled. The only thing that is agreed upon is that genetics and environment interact in complex ways to make each of our dogs unique.
The good news is that there are lots of proven treatments for canine mental disorders. These range from environmental enrichment and lifestyle changes, to nutritional supplements and medications.