A theory on the relationship between the Fall, and suffering today
The Bible says there is a strong relationship between the Fall and suffering:
Romans 5:12: For this reason, as through one man sin came into the world, and death because of sin, and so death came to all men, because all have done evil
Here is a theory of how suffering, death, and sin could be related. It has a few problems, but maybe there is something in it to answer questions in a genuine way.
A while ago I was reading an online comic and in it one character was trying to justify the existence of hell. But instead of saying 'God is a God of justice' or 'God gives us the freedom to reject Him' the character said that the reason for hell was something like: 'God will not allow sin in His presence, because He is a good God'. I thought that was an interesting response, because 'God not allowing sin in His presence' because of His goodness would seem to have nothing to do with hell and suffering, depending on your view of hell.
Later on I got into reading about the philosophy of mind and consciousness. Consciousness is what you feel when your brain processes information. Whatever consciousness is, it seems different from our physical brain. It seems to exist in a 'mental world' quite different to the world of e.g. tables and chairs. Debates in the philosophy of mind are about how a 'mental world' arises out of a physical world.
Thinking about the philosophy of mind, one interesting idea is to say that there are two worlds that humans live in: a physical world and the mental world. So instead of trying to figure out how the mental arises out of the physical, you can sort of give up and say that humans are a combination of the physical and the mental and the mental is in its own world with its own rules. The mental is based on the world of God.
You know that phrase 'God will not allow sin in His presence, because He is a good God'? Imagine that in the mental world, either a mind is connected to God or it's not. If it's not connected to God the mind suffers horribly. The problem is that when we do something wrong, God needs to separate Himself from our wrongdoing, and that means that God has to disconnect our mind from His. This means that sinners' minds get disconnected from God, creating horrible suffering, even if physically everything is fine, and there are no diseases, tornadoes, tsunamis, nothing of the sort...
So physically, God can stop any hurricane, earthquake, disease, accident, anything. But God cannot stop pain, terrible, unrelenting pain, if a mind is not connected to Him in the mental world. Because that's what it feels like for a mind not to be connected to God in the mental world: death and pain.
Somehow, if God remained connected to a mind that wants to do wrong, then God Himself would be 'infected' with sin. Or maybe it's not a matter of choice, and God simply cannot be connected to a mind that wants to do wrong. Either way, you can explain how horrifying pain must exist in a world where there are people who do wrong, even though God is perfectly good and all-powerful.
There are a few big issues here:
1) Animal suffering. They don't really do wrong because they aren't morally responsible. Yet there's a lot of suffering in the animal world. The Bible does say that the animals were subjected by God to the pain that humans are under (Romans 8:19-22), but why?
2) So maybe getting disconnected from God causes pain. But it sure seems that viruses cause pain. One way of getting out of this problem is to say that the pain has to be there anyway, and God chooses to make it look like physical stuff causes the pain. This seems a little bit odd and counter-intuitive... God needs to have a reason to make it look like e.g. earthquakes cause pain when actually our mind getting disconnected from God causes pain. God doesn't add to our pain by making it look like it's the result of e.g. diseases, so at least that aspect makes sense.
3) Suffering is a universal fact of life, and there isn't anyone who doesn't experience it. OK, but some people suffer a lot more or less than whatever is 'average'. Why? This remains a bit of a mystery. Maybe suffering gets 'balanced out' over an eternity, assuming a person doesn't have their sins removed by Christ - Luke 6:24?
On the good side, this theory does fit in with Luke 17:20-21, which talks about what the Kingdom of God involves:
Once, having been asked by the Pharisees when the kingdom of God would come, Jesus replied, "The kingdom of God does not come with your careful observation, nor will people say, 'Here it is,' or 'There it is,' because the kingdom of God is within you."
If suffering happens because our mind gets disconnected from God, then perfect happiness will come when our sins are completely removed by Christ. Because we have never experienced life having our mind connected to God, then this theory explains why heaven is going to be so wonderful, even if it sounds to a non-Christian like it's just a change of scenery. They might ask: what's so great about heaven, just because it looks beautiful? The great thing about heaven is that our soul/mind will be connected to God for the first time, and we will experience life as it was originally meant to be experienced - in union with our creator, feeling the happiness that the image of God was originally meant to feel. We cannot even imagine what this is like - if we could, our mind would not be currently disconnected from God due to sin.
It also explains why no matter how much God helps those who reject what Christ did for them, they must suffer forever if they continue to reject Christ (very reminiscent of CS Lewis' Great Divorce).
In summary, you could say that the theory works like this:
Do we suffer because of a greater good? Yes.
1. Either we are perfect and there is no suffering.
2. Or we are morally imperfect and God becomes evil, because God allows sin in His presence/does not separate Himself from a soul that does wrong.
3. Or we are morally imperfect and there is horrible suffering, but God is perfect and provides a way for us to be free from sin and be truly happy one day (through the cross).
The third option is the best, which is what we see God doing. For the greater good of God remaining free from wrongdoing, we must suffer, assuming this whole system regarding a 'mental world'.
[See comments for clarification]