Yes, You can file return even after the due date is gone.
However, in case you have some tax due to be paid to the government, you will have to pay penal interest @ 1% per month for late filing on Tax Payable amount in addition to interest payable for late payment of taxes.
Apart from due date, there is last date of filing the return also. Last date for filing of any IT Return of Financial Year, will be last day of next to next financial year. For example, in case you have not filed your Income Tax Return for the financial year 2013-14. The due date for this will be 31st of July, 2014. And last date of filing will be 31st March of 2016.
As per Amendment in Finance Act 2016, Last Date to file Income Tax Return for FY 2016-17 will be the last day of the assessment year. So you will not be able to file your Income Tax return for FY 2016-17 after 31st March 2018.
Beyond which the return will become time barred and you would not be able to file the same. Assessing Officer may require you to pay penalty up to Rs.5,000 for late filing of Income Tax Return where return is filed after the end of the assessment year.