Do you have customs that go accompanied with welcoming the new year?

When better to ask this question then on the changing of the old to the new year?
My girlfriend is Greek and just an hour ago we symbolically sweeped all rooms and other spaces clean with real brooms while singing a song (“the old year went away, a new year has come, with music and presents”) and on top of that we broke a plate (because we didn’t have a pomegranate).

Are there customs in your country or state, or even in your family?