When thinking about examples of artificial creatures, one of the first things that popped into my mind is the fictional robot Marvin, the Paranoid Android, from the hitchhiker's guide to the galaxy books. 

He's designed as a personal assistance robot, usually given simple tasks such as opening doors or making coffee. However, he's been given a vast amount of intelligence that he never gets to use, meaning he experiences existence as permanent boredom and depression. He doesn't seem to be programmed to have any creativity or freedom to decide what he does with his intelligence, and no-one can give him satisfying tasks (in fact, he's turned into a theme park attraction for a while where people are challenged to make him happy but never succeed). 

As someone who's struggled with depression a fair bit, I'm quite interested in what causes it and what does and doesn't help. I haven't had much luck finding an real-world application of a robot that exhibits depression symptoms, though. 

Marvin's depression is interesting, because it reflects a real depression fairly well: It seems like all he needs to do is get up and find something to do that is worthy of his massive brain and all his  problems are solved. Depression in humans (well, in me anyway) work similarly: The best cure is to get up and do stuff, take up projects, work out, clean your house, etc. In a depression this is difficult, because it blocks your interest/enthousiasm/motivation to do these things. That's one of the harder parts of depression to communicate to someone who's never experienced it. Reading about Marvin makes it obvious why the problem persists; he's not programmed to be creative or motivated enough to do his own thing. It illustrates how futile a depression can feel. 

I haven't found any examples of real artificial creatures that try to express depression, if they exist I'd be interested to see how it's done.