If you want an absolutely serious answer, I guess I can attempt to give one.

In the Judeo-Christian system, animals are generally believed to become nonexistent when they die, because they don't have souls. Think of God as a geometric Line, no beginning, no end. Humans are rays, they have a beginning, but their souls live on into eternity. Animals are line segments, a specific beginning, a specific end.

As for eastern religion, Animals in most cases are just incarnations of souls, and if the animal lived a good life, will be reborn as a human or higher tier animal.

As for atheists, because you seemed to pose the question to them as well, not only do they not believe in heaven or hell, but most don't believe in right or wrong either, only moral relativism. In this system, it's impossible to be "good" or "bad," so there's really no unfairness in them dying and not going anywhere.

I hope that answers your question better than the new age hippie crap/undeducated theology that's been posted so far in the topic.

__________________
Oh well she bore all her parts but she never was found
You think "I'll carve a path through New York and be an artist", but are you anything?
Then you find out you can't ask a baby to cry
And an obsession with the past is like a dead fly
And just a few things are related to the old times
Then we did believe in magic and we didn't die
It's not my words that you should follow it's your insides
You're just an inside
Adjust your insides
You're just an inside