An important event that happened in 2007 was Argentina elected its first female president. Other events in 2007 included the announcement of the iPhone, the disappearance of Adam Air Flight 574, and the discovery of the tomb of Herod the Great.
The biggest world event in 2007 is debatable. In the US, the last Harry Potter book was released, which was a huge event. The mortgage crash began in 2007 and there were huge breakthroughs in stem cell research. The Virginia Tech tragedy took place in 2007 and so did the Saffron Protests.
There are a number of important world events that occurred in 2007. On the first day of 2007 alone: Slovenia changed its currency to the Euro, Bulgaria and Romania Joined the EU, and Ban Ki Moon took over from Kofi Annan as UN Secretary-General. For more events see http://en.wikipedia.org/wiki/2007