There may exist special circumstances that require you to file in a timely fashion, but I'm not familiar with any scenarios for individual tax returns. In general there is no penalty for not filing on time so long as you don't owe, and no need to file an extension.
If you're claiming a refund, you have 3 years to file your federal return, so today would be the last day to file your 2014 return and get a refund. New York's e-file site shows that you can currently e-file 2014, 2015, and 2016, so it seems like they have the same 3 year deadline.
There technically is no limit on filing old returns that I'm aware of, but if you should have been filing for the last decade, the IRS would typically only request you file returns for the last 6 years and then would work out a payment plan for back taxes due.