There is an entire field of theology devoted this (theodicy) and there must be more than a hundred "solutions", some of which actually do have a certain amount of internal logic. A lot of the major ones have to do with god allowing some amount of suffering/evil for the "greater good". There's one I kind of like in which every bit of suffering here on Earth is actually useful because it piles up on a scale in Heaven somewhere and does...something or other, I forget what, outweighs evil at the end of days or something. e.g. suffering is useful in a way that we do not know. There's another that posits that even for some of us to just see or hear about suffering makes us think about it and makes us better people further down the line. So, say a little innocent girl dies horrifically at the hands of a sadist; the rest of us hear about that and are appalled, and think about it, and maybe we live better lives as a result. Most of the "solutions" boil down to it's-for-the-greater-good ideas like this, and that we wee humans just don't have enough perspective to see the Big Picture that god is seeing.

Of course there's no way to disprove this; there's also no way to disprove any of the alternate hypotheses (god may very well be omniscient and benevolent, but not omnipotent, for example) and there's no way to disprove that the FSM isn't behind it all, either, and there's no way to disprove the idea that evil is caused by Zeus and Thor zinging random lightning bolts at each other and missing a lot because they're always too drunk to aim right. There's an infinite number of equally silly, equally internally consistent, theories of evil.

I have to also mention my favorite version, which is a really cool inverted version that posits that god is actually 100% malevolent, and that thus the real question is, why does god occasionally allow good things to happen to people?