Is there a Feast day for every day of the year?

           
           Well, yes and no. The official Roman calendar of feast days for celebration by the Universal Church (in other words, all over the world) does not have a saint's feast day every day. The Church chooses saints to be celebrated worldwide very carefully -- they must have a strong message for the Church as a whole. That doesn't mean that other saints are somehow less holy -- although some of the saints that have been dropped were legendary and there is little evidence they existed.
Religious orders, countries, localities, and individuals are free to celebrate the feast days of saints not listed on the universal calendar but which have some importance to them. And there are indeed feast days for saints every day of the year. As a matter of fact there are at least three saints for almost every day.
Butler's Lives of the Saints has the most complete listing of saints' feast days I have found, though I advise care in choosing the edition. Recent changes have been made to the calendar that would affect feast days.