The last day to file your income taxes is April 15th. You can file a form 4868 for an automatic extension of time to file. This will give you an additional 6 months to file but any tax owed must be payed by April 15th to avoid penalty.
April 15th is the last day to file your taxes. And they are actually due on April 15th, so you might consider filing in your local personal tax office.
The last official date to file taxes is October 15 after the current year. Payment is due on April 15, so a late filing is OK, but you will owe a small financial penalty and interest on your tax due.