I imagine it would be harder than for humans, most animal species not being tool-making - on the other hand, some animals, like a scorpion, for example, have the tools with which to cause their own demise.
The first person who mentions lemmings is gonna get such a slap.
On the serious side, some marine biologists have speculated that whale beachings might sometimes be deliberate suicide attempts. Some animals have been known to starve to death as a result of a refusal to eat, in apparent mourning for a lost companion. Whether this can be considered suicide is up for debate.
I would think no. There are some animals that may engage in behaviors that result in their own death (i.e. a bee that has stung) but these behaviors generally have some higher purpose for the species overall. There would be no evolutionary benefit to any species that could complete suicide. Furthermore, the animal would have to have a concept of death, and I don’t believe that animals have the level of intellectual functioning to allow them to comprehend their own death.
The first thing you need to do is define “suicide.”
A large number of samon that travel from the ocean to their birthplace to breed die. This could be considered suicidal behavoir.
There are species of spiders were the male lets the female eat him after mating. Is the male spider committing suicide or providing nurishment for his offspring?
(When it comes to sex, humans have very little to complain about.) 
Animals are instinctively survivalists and will do anything to avoid dying. I would think that this means they have some concept of death, even if it’s purely visceral. I would also think that the survival instinct would also preclude even the consideration of suicide.
I suppose it’s possible however that intense psychological trauma (such as paralyzing fear or some other kind of stimulus overload) may affect their judgrement or even suppress instinctive response – a deer caught in the headlights, for example. But that’s just a WAG.
Animals are instinctively survivalists and will do anything to avoid dying. I would think that this means they have some concept of death, even if it’s purely visceral. I would also think that the survival instinct would also preclude even the consideration of suicide.
I suppose it’s possible however that intense psychological trauma (such as paralyzing fear or some other kind of stimulus overload) may affect their judgement or even suppress instinctive response – a deer caught in the headlights, for example. But that’s just a WAG.
S.E.D. I checked this thread to disavow anybody of that notion, and tell them Disney fudged the facts on a movie, imagine that.
There are pets that starve to death after the human dies.
There are animals ever so often in the documentaries that pine away when a mate is killed. They seem to get over the dead babies, before they starve.