Suffering implies there is pain. How can there be any value in this? The only good that can arise from suffering is if we look deeply to the root of our suffering and learn from this. Then suffering becomes a significant teacher.
It does seem that sooner or later all beings experience suffering, in small and larger ways and eventually we all die which can be seen as the ultimate suffering if we are not prepared.
We do much to try and eliminate suffering but so often our attempts to avoid suffering simply bring about different suffering. It seems the major pursuit of human beings is happiness.
When I look at the causes of suffering, I see there is no simplistic answer - like 'oh, it's my karma (speaking of which I received a beautiful response to a question about karma from True Eloquence)
So much of our suffering seems to arise from our response to situations and if we learn to see things differently, the suffering falls away.
Some of our suffering is a result of how we've lived out our lives and although we may not be able to change the outcomes, we can learn from our history and avoid similar situations in the future.
There is also physical suffering, such as great pain in the body, say from genetically inherited illness, when we may need to learn how to live with suffering as a companion and acceptance seems to be a crucial attitude.
Sometimes there's the suffering which comes from natural disasters - our homes may be swept away, we may lose loved ones or be injured. Suffering then reveals to us the temporary nature of life. An awareness which can grow from this is to live fully and make the most of precious short time we have to learn.
Suffering so often can be the result of attachment and it is only in the letting go that relief can be found. Such as when something we love breaks or when a beloved dies.
I never thought deeply about the why's of suffering until I encountered Buddhism. Here is a link re Buddhism on suffering (there are many links - I selected this one randomly).
"Whatever joy there is in this world
All comes from desiring others to be happy,
And whatever suffering there is in this world,
All comes from desiring myself to be happy.
Bodhicitta is a precious path where we change our focus from our suffering to the suffering of others as so beautifully described here ( http://buddhism.kalachakranet.org/compassion.html ) in this prayer by Shantideva
"May I become food and drink in the aeons of famine for those poverty-stricken suffers.
May I be a doctor, medicine and nurse for all sick beings in the world until everyone is cured.
May I become never-ending wish-fulfilling treasures materialising in front of each of them
as all the enjoyments they need.
May I be a guide for those who do not have a guide, a leader for those who journey, a boat
for those who want to cross over, and all sorts of ships, bridges, beautiful parks for those
who desire them, and light for those who need light.
And may I become beds for those who need a rest, and a servant to all who need servants.
May I also become the basic conditions for all sentient beings, such as earth or even the sky,
which is indestructible.
May I always be the living conditions for all sentient beings until all sentient beings are
May all beings practice loving kindness