Intro: Why do bad things happen to good people? For that matter, why does anything happen at all? Is there cause and effect?
The assumption of the High Holidays liturgy (ie. the Machzor) is that God is actively involved in the world and our own personal lives. It's not so straightforward in other Jewish sources.
This assertion of God's involvement creates a number of different theological problems:
1) Theodicy: If God is loving, omnipotent, and omniscient - why do we see so much evil happen in the world? Related: Tzadik v'Ra Lo - Why does someone who is righteous suffer? Shouldn't she enjoy the rewards of her righteous living? Similarly, why do some evil people seem to prosper? Shouldn't they suffer instead?
2) Free Will - If God is so actively in our lives and world history, and God is Omnipotent, doesn't that result in a lack of Free Will?
Eliezer Berkovitz, Faith After the Holocaust - Hester Panim & Free Will
"Not for a single moment shall we entertain the idea that what happened to European Jewry was divine punishment for any sins committed by them. It was injustice absolute. It was injustice countenanced by God. But if we hold onto our faith in a personal God, such absolute injustice cannot be a mere mishap in the divine scheme of things. Somehow there must be room for it in the scheme in which case the ultimate responsibility for this ultimate evil must be God's."
"Such is God. He is a God who hides himself. Man may seek him and he will not be found; man may call to him and he may not answer. God's hiding his face in this case is not a response to man, but a quality of being assumed by God on his own initiative... God does not determine in advance that one person be a Tzadik (a righteous person), and another a Rasha (a wicked person). But unless the possibility existed for a man to be a Rasha, if he so desires, one could not only not be a Rasha, one could not be a Tzadik either...
God cannot as a rule intervene whenever man's use of freedom displeases him. It is true, if he did so the perpetration of evil would be rendered impossible, but so would the possibility for good disappear... If God did not respect man's freedom to choose his course in personal responsibility, not only would the moral good and evil be abolished from the earth, but man himself would go with them. For freedom and responsibility are the very essence of man. Without them man is not human. If there is to be man, he must be allowed to make his choices in freedom. If he has such freedom, he will use it. Using it, he will often use it wrongly; he will decide for the wrong alternative. As he does so, there will be suffering for the innocent."
"Unlike other authors (Soloveitchik, Berkovitz) who see hester panim (the hiding of the divine countenance described by the prophet Isaiah) as a temporary suspension of God's surveillance, Birnbaum sees it as a necessary and inexorable development in the cosmic plan. There is according to Birnbaum a primary form of hester panim in which God contracts his real time consciousness and curtails individual providence in order to further the realization of mankind's full creative potential via his ascent in knowledge and freedom. Like a parent who has the power to watch over his child when he is away from home, even without the child's knowledge, yet who refrains from doing so in the interests of the child's own growth and development, God must (though it is painful both for us and Himself) curtail His own realotime surveillance and suspend individual and historical providence, for the greater interest and providence of humanity as a whole. - The Jewish Reivew, God and Evil: A Unified Theodicy / Theology / Philosophy by David Birnbaum.