no longer believe in god, but here's a few things i was taught about this question when i was still christian:
god allows suffering and illness because he works in mysterious ways. this is just a very lazy blanket-response. personally, i would hate to be the five year old toddler getting massacred by a semi-truck on a thursday afternoon for a reason god won't elaborate on. but that's just me.
god allows suffering and illness as a test of our faith. this, of course, is the deeply egocentric view that other people's suffering is actually about you specifically. god gave grandma cancer because everything in your life happens for a reason, and he's putting you through the pain of losing grandma because you have to learn a lesson or pass a test of some sort in the eyes of god. it's the false belief that, actually, everything revolves around you and your faith. the reality is that grandma getting cancer was about grandma, and not you and your sorrows.
god allows suffering and illness because of our sinful nature. personally, i think this is judgemental as fuck. imagine being a god, an all-powerful creature, who created weak-willed humans that are supposed to worship you, and should they fail due to the flawed nature you created them with, they must now be subject to great suffering and pain. in other words, imagine having an ant colony, placing an apple slice in the ant colony's cage and then smiting the ants for eating the apple slice. nonsense.
god doesn't WANT to allow suffering and illness, but the devil causes it anyway. even when i was deeply faithful and christian, i thought this was a weird one, since god is supposed to be all-powerful and much stronger than the devil, yet he gets overpowered at influencing his own creation on earth, by a fallen angel with a fraction of his power, apparently.
god allows suffering and illness because we have free will and therefore actually do it to ourselves by choice. we choose to be sinful, we choose to be horrible to each other, and suffering and illness are the logical consequences. again, i think it's fucked up that god would create us in such a flawed way and then get really upset at us for being flawed. that's not a god i would worship.
the bottom line, the reality, is that god had no choice in the matter, because he doesn't exist (at least, not in the biblical sense - maybe there is a creator, but it's obvious that suffering and illness have nothing to do with him or how he feels about us).