Is there any documented evidence for suicide among vertebrates other than humans? Lemmings not accepted !
Well, there are certain behaviors that may qualify. The clearest example I know of would be sexual cannibalism, and more specifically (source):
The redback spider is one of only two animals to date where the male has been found to actively assist the female in sexual cannibalism. In the process of mating, the much smaller male somersaults to place his abdomen over the female's mouthparts. In about two of three cases, the female fully consumes the male while mating continues. Males which are not eaten die of their injuries soon after mating.
That sounds pretty suicidal to me...
A less flagrant but commoner example is that of mothers dying to nourish their offspring. Again often seen in spiders, the best example I know of is the giant pacific octopus (Enteroctopus dofleini). The female will chose a den and lay her eggs. She will then spend her last weeks tending her young, never leaving the lair to hunt. Eventually she dies of hunger and her body nourishes her young. My source here is the wonderful BBC life documentary series.
Neither of these are vertebrates of course but still, I thought the suicidal little spider was interesting.
The problem is that committing suicide, using the commonplace definition of it, would require an understanding of death. I am sure that an animal can have a basic understanding of the death of others, so far as they realise the difference between a living companion and it's dead body. But if they understand that this lifeless body will never go "back to normal" again and that there is also future death for themselves, I am not convinced. So, without the understanding of the own, irreversible death, there is (following the definition) no suicide.
According to this article whales could kill themselves by swimming to the beach and even when pushed back to the water, they return or dogs can drown in the water when suffer a lot.
As Zoobiquity points out, gorillas sometimes die from self neglect (starvation) caused by clinical depression. These, besides humans, are likely the only animals to do so through self-neglect.
Then again, one could call scrapie (a prion disease in sheep) or tail-plucking disorder (in parrots and other birds) and other self-mutilative disorders as a form of suicide, but the actual wounds themselves aren't liable to kill the animal.