Yes, there are a lot of studies (and even more anecdotal stories, of course) confirming the benefits of pets for your mental health. What's surprising is that even people suffering from serious cases of depression, schizophrenia, and other conditions can find solace in their furry (even non-furry, such as goldfish!) friends. Besides providing unconditional love and support you may not get from other people, or at least not feel like you're getting, pets help you keep connected to the world in some way or another. It's much harder to stay in bed all day when your dog keeps pestering you to play, for example. They also encourage you to go out, engage in some physical activity, and interact with other people.
Yes, Having a pet is good for our emotional and mental well being.