The scriptures contain three main explanations for suffering:
1. God punishes those who disobey him.
In this case, God causes the suffering.
Example: Israel is defeated militarily and taken into captivity by foreign invaders because they did not worship YHWH correctly (or some other god).
2. God allows suffering to happen because of the sin of others.
In this case, people cause suffering, and God allows it but does not directly cause it.
Example: A king of Israel is wicked, and Israel is defeated militarily and suffers because the king is not faithful (even though people individually might not have sinned and deserved to be killed/enslaved)
3. Suffering exists to foster a greater good.
The cause is a combination of the above two, but is directed in both cases by the will of God to enlighten people or to bring about a greater good.
Examples: Christ did no wrong, but he suffered to bring about the atonement for others. The apostle Paul suffered in order to prove that he was a true disciple of Jesus Christ (his own viewpoint in his letters). And in Mormon theology, we suffer in our life so that we will learn lessons (a process of enlightenment).
I posit a fourth explanation from my current view of existence:
4. We suffer collectively, as a people because we want suffering more than not suffering.
We will suffer and cause suffering until we decide (collectively) to stop. This is very similar to #3, except that it doesn't require a central authority (God) directing and orchestrating the suffering. In my own view, we can decide to no longer suffer. We can still experience physical pain, but spiritual suffering is a choice we make. We experience and cause suffering by wanting something else (anger, violence, revenge, theft, etc.) more than peace.
I recognize that there is suffering that falls outside this fourth explanation (particularly that suffering which occurs strictly as a result of the physiology of The Fall, like depression and numerous disabilities of varying kinds, which we did not choose and over which we often have limited control), but I really like the overall idea that we do have a degree of control over our "suffering" - especially through an Atonement theology that posits a God who has suffered all we suffer in order to know how to succor His people in the midst of their suffering. This allows us to turn our suffering over to Him who has suffered already and not let our natural, unavoidable suffering define who we are and can become.
I also love the implication that it is fine to look for ways to alleviate sufering - like medications for depression, for example.