It depends on your location.
The only day that the major UK and US newspapers are not produced is Christmas Day. So yes in the UK and US they will be available on New Year's Day.
For any other country, re-ask the question with the missing information.
There were and still are newspapers published on Christmas day, in countries where Christmas day is not a holiday, or not a major holiday. And in these days where versions of newspapers are published instantly, on-line, arguably most are being edited and published in some form on Christmas day.
As for whether there were ever printed newspapers on Christmas day in your country... it probably depends your country. Perhaps a more interesting question is, "How long has Christmas day been a public holiday in [UK/USA/Ireland/France/Sweden/wherever...]?"
It was a tradition to do Christmas day newspapers since 1965. but that stopped in 2000 and now there are no papers on Christmas. There are also no papers on New Year's Day Good Friday Easter Sunday Easter Monday Bank holidays and Boxing Day
Christmas day originally was on the day of Christmas
In 1968 Christmas Day was on a Wednesday In 1969 Christmas Day was on a Thursday In 1970 Christmas Day was on a Friday In 1971 Christmas Day was on a Saturday In 1972 Christmas Day was on a Monday In 1973 Christmas Day was on a Tuesday In 1974 Christmas Day was on a Wednesday In 1975 Christmas Day was on a Thursday In 1976 Christmas Day was on a Saturday In 1977 Christmas Day was on a Sunday In 1978 Christmas Day was on a Monday In 1979 Christmas Day was on a Tuesday In 1980 Christmas Day was on a Thursday In 1981 Christmas Day was on a Friday In 1982 Christmas Day was on a Saturday In 1983 Christmas Day was on a Sunday In 1984 Christmas Day was on a Tuesday In 1985 Christmas Day was on a Wednesday In 1986 Christmas Day was on a Thursday In 1987 Christmas Day was on a Friday In 1988 Christmas Day was on a Sunday In 1989 Christmas Day was on a Monday In 1990 Christmas Day was on a Tuesday In 1991 Christmas Day was on a Wednesday In 1992 Christmas Day was on a Friday In 1993 Christmas Day was on a Saturday In 1994 Christmas Day was on a Sunday In 1995 Christmas Day was on a Monday In 1996 Christmas Day was on a Wednesday In 1997 Christmas Day was on a Thursday In 1998 Christmas Day was on a Friday In 1999 Christmas Day was on a Saturday In 2000 Christmas Day was on a Monday In 2001 Christmas Day was on a Tuesday In 2002 Christmas Day was on a Wednesday In 2003 Christmas Day was on a Thursday In 2004 Christmas Day was on a Saturday In 2005 Christmas Day was on a Sunday In 2006 Christmas Day was on a Monday In 2007 Christmas Day was on a Tuesday In 2008 Christmas Day was on a Thursday In 2009 Christmas Day was on a Friday In 2010 Christmas Day was on a Saturday In 2011 Christmas Day was on a Sunday In 2012 Christmas Day was on a Tuesday
In England people do open presents on Christmas day, the day after father Christmas has come
Yes, UK newspapers will be printed and sold on Boxing Day.
On Christmas Day, you do not not celebrate Christmas =D
Christmas eve and Christmas day
Eve means "before" and naturally Christmas Eve is the day before Christmas.
Christmas Day will be on a Wednesday in 2013.
It is Christmas Day. The "D" is capitalised as it is part of the full name.
On the day after Christmas Eve, Ireland celebrates Christmas Day.
Yes there are... newspapers have been published as normal.
Some People have Christmas dinner on Christmas day and some people eat it on Boxing day