Sad to say, most often it gets written as "Fathers Day." We Americans have for some time been throwing in apostrophes where they don't belong (e.g., CDs, 1960s, shoe's) and leaving them out when they're called for (e.g., "In the 1960's there were no CD's or iPod's so when it came to kids entertainment, mother's had to rely on the childrens TV show's.) (Sigh)