I don't think non-human animals perceive time and death like we do. Therefore, I'm not sure that suicide would be the proper term for it. However, yes I do think all animals are capable of self destructive behaviors, as well as sacrifice of their lives. Many animals can suffer from similar psychological disorders that humans do (Working with abused and neglected parrots is much like working in a psych ward at a hospital.) I've seen things like OCD, self-mutilation, depression, innability to focus, etc. However, I'm not sure non-human animals make the decision "Death would be better than this" in the same capacity that humans can. Usually, in situations of sickness or injury, the animal is considering the greater good of the pack, rather than itself.
Much of what we consider suicidal behavior in animals is accidental I think. Things like flying into windows or walls, or running into the middle of the street for example.