It's no secret that there are some pretty difficult passages in the Bible. The punishments for some sins seem harsh, and sometimes we don't even understand why things are sins. But by far the greatest objection to the Bible is when God commands the Israelites to wipe out entire nations. It's hard to understand why God would give such commands. But when we look a little deeper, we start to understand.
First, we must note that God didn't just obliterate them instantly. In Genesis 15:16, we see that "...the iniquity of the Amorites is not yet complete.". In other words, God didn't pull the Jews out of Egypt and have them attack these people until they were literally as bad as they could possibly get.
How bad is that exactly? As we see in Psalm 106:34-38, it's not quite as simple as pinching a few pennies from the charity box. These people were so grotesque that they actually slaughtered their children to their gods. That on its own should be enough to convince us that these people deserved to die, but then we come to the worst part. The Jews, this nation chosen to be God's beacon to the world, these people created to preserve his word, this culture through whom the Messiah himself would arise, ended up taking after the very barbarians they were commanded to destroy. In other words, the continued existence of the nations God commanded Israel to destroy could have changed the course of history and threatened the salvation of humanity.
Now, ultimately, we have no need to justify God. Indeed, we have no right to justify God. We don't get to decide whether or not His ways are just, because we don't judge Him, He judges us. But when we look at what happens when His commands are disobeyed, we see just how important it is to obey Him, even when it seems grotesque to us.
This, of course, makes perfect sense when you consider God's omniscience. His knowledge of not only the future, but indeed all possible futures, allows Him to see what will happen if He gives, or does not give, certain commands, as well as how His own actions, or inactions, will affect us. His great wisdom not only allows Him to know how He designed the world, but what happens within that particular system. In short, just as a child may find his parent's commands confusing, or even restrictive and cruel, yet the parents know what they're doing, so also does God know what He is doing, even when His commands seem odd to us.
Ultimately, Scripture tells us that while God will absolutely destroy the wicked, it brings Him no pleasure to do so. When His image bearers fall into sin, He desires their repentance, and He will not destroy those who repent. However, because He is Holy, He must deal with sin. His solution, therefore, is to divide humanity into two categories: The wicked, whose sins are retained, and the righteous, whose sins are forgotten. The distinction is faith. Specifically, faith in Jesus, His Son. Jesus became a human being, lived a perfect life, died on the cross, and rose again. When He died, He received the full wrath of God for sin. When He rose, He brought eternal life to all who will repent and believe. Everyone else, sadly, will perish.