Second, what about all the Christians in those places? In the Old Testament, didn't God spare Israel from judgment at least because of the remnant of faithful God-followers? Since the Bible says God never changes, shouldn't we expect that He would at least offer mercy because of a faithful few?
Third, the Bible is very clear throughout the Old Testament and especially in the New Testament about God's grace - that He is being patient and restraining His judgment (see 2 Peter 3:9). And Romans 2:4 says it is God's KINDNESS that leads people to repentance. So if God wanted people to turn from their wicked ways, it would be in keeping with what the Bible says for Him to draw people to repentance through His kindness, not harsh judgment.
Fourth, if these are God's judgment, you have to ask - where was the forewarning? Throughout the Bible God always gave people a chance to repent before bringing judgment and destruction; Jeremiah, Isaiah, and Jonah are great examples of that. When did the people of Japan and New Orleans - as a whole, not just as individuals - receive a warning to repent? For God to bring punishment without first bringing a chance to repent seems very out of character for God; it would make it seem like God is a schizophrenic.
So could these events be God's judgment? Yes, that's possible. God is sovereign and is good and right and just in everything He does. If He were using these events to bring judgment, because He is God He has every right to do that and we cannot accuse Him of being unfair or unjust. BUT - from what the Bible says about how God chooses to relate to us right now in the age of grace and in the new covenant because of Jesus - I would say these things are probably not God's judgment.
So why do these things happen? Because we live in a broken, messed up world under the curse of sin where although Jesus is King over all, stupid satan still has some power as the prince of darkness. So I would attribute these horrible events to what Romans 8:19-22 says: these are the tragic effects of sin being played out in creation, but probably not the judgment of God.