Quotes taken from http://wiki.answers.com/Q/Do_any_animals_other_than_humans_commit_suicide (it's a long article and worth the read)
How can you deny the numerous stories of animals who deliberately hurt themselves when put in captivity, or pets who starve themselves and die after the loss of their master? The animal puts it's life in jeopardy because it is 'unhappy.'
Whether this is conscious or unconscious is the question at hand and whether this 'unhappines' leads to death, or suicide is hard to prove.
Suicide, with regards to a seemingly deliberate action ending one's life with no other apparent purpose, is regularly engaged in by many species of animals (see some examples in the next section)- the contentious issue is whether those creatures genuinely understand the concept of death, and that their actions will result in it- that is, while the action itself may have been apparently deliberate, we can not know for certain if the desired effect was deliberately suicide (and not, for example, merely self harm).