This statement is always translated wrong. Not always, but often. It is often translated as "God is great!" However, from what I understand and much research into it, it should be translated as "God is greater!" or "God is greatest." Some would say what's the difference? But here's what I think.
Watching Fahrenheit 9/11, there was a woman with a demolished house and she is shouting various things such as "So this is American democracy?" (in essense) and then she shouts "Allahu Akbar!" and it is translated in subtitles as "God is great!" I don't like this as it doesn't make sense. Why would she shout "God is great!"? What she is shouting is "God is greater!" God is greater than all of this, this world, and everything happening. With God there is Justice. If she were saying "God is great!" it doesn't have the same meaning. If she said "God is great," she would be saying that her house being demolished is a sign of God being great, but what she is saying is that "God is greater" than all bad or good that is happening in the world.
Allahu Akbar! as explained in the book The Underlying Concept of Daily Prayers by Ayatullah Sayyid Ali Khamene'i:
With this statement the worshipper begins the glorious proceedings: with such a splendid opening. ALLAHU AKBAR (God is Greater).... Greater than what we can imagine, Greater than all other gods worshipped by people in the course of history. Greater than all the powers and forces which man will be frightened of or terrified by and expected to get support and energy from. Greater than one would dare disobey or break His laws.
This is the context in which she was saying the words (I believe). This small misinterpreation changes the whole meaning of what she was saying and it really bugs me that it's not translated correctly in many cases (in Islamic books as well as others).