Surely it depends how many fathers you are talking about.
The US government has stated that Father's/Mother's etc is correct because it is a day for each person to celebrate just one person. All the commercial cards I have seen say Father's ....just one Father each!
But when writing about the Day as a day for all Fathers it would be Fathers' Day
There is also the argument that as Fathers do not own the day it should have no apostrophe.....
Oh Bags, these threads have made me paranoid I'm ok with the 'if a word is missing' apostrophe, but the possessive plural/single one throws me into confusion!