I don't know if this can be considered an event but the Myer Christmas windows are always great to visit with the kids. It's different every year and really brings out the festivity. The Chinese New Year celebrations are also very exciting where everyone from all parts of Melbourne come into the city to join in, celebrate and to enjoy the lovely food.
I find the New Year's Eve fireworks on 31 Dec at Federation Square is the best free event of the year. Yarra banks and docklands offer excellent vantage points for viewing fireworks and everyone can join in the new year's celebrations. Diwali Festival is another excellent free festival at Federation Square taking place in October which woos all Melbourne into jubilant celebrations.
Watching the New Year's fireworks at Flagstaff Gardens was quite amazing. Melbourne White Night was really good too, with throngs of people heading to town and being engaged in different types of arts activities and performances.