This depends, of course, on what country you live in. There were major elections in many countries, including the US, Australia, Portugal, and others. There were various disasters and coups and such.
On a worldwide scale, perhaps the most important event of this year was the Dunblane massacre in Scotland. This was a shocking event in which a man killed 16 children aged 5 or 6 years old. It gained worldwide attention because of the age of the children and the number of victims. There was also a mass killing in Australia that year which got less attention because its victims were adults.
Another event that got a lot of attention that year was the birth of the first cloned sheep. This was the sheep that was named "Dolly." She was cloned and born in the UK.