The standard spelling of the holiday that falls on February 14th is Valentine’s Day. Valentine is singular and possessive, so it takes an apostrophe s. This is how it is spelled in edited writing everywhere.
The day is named after Saint Valentine. It is his day, hence the possessive. Because there has been only one of him, it wouldn’t make sense to pluralize his name. Of course, one could argue that Valentine now has two alternative senses in which it can be plural—namely, (1) the person one loves on Valentine’s Day, and (2) a Valentine’s Day card—and in light of these, it might make a little sense to spell the holiday Valentines Day. Nevertheless, the form with the apostrophe is the more common one by a large margin.
The ngram below graphs the use of Valentine’s Day and Valentines Day in a large number of English-language texts published between 1900 and 2000. The spelling without the apostrophe has gained a little ground but still hardly competes against the more common form.