As of 2017 is it still possible to get a transaction confirmed without a fee? In the past it was possible to get a transaction without a fee confirmed if the inputs and outputs had a high enough priority and followed some rules. As of 2017 is a "free" transaction still possible if you don't care about how fast it will be confirmed? Several hours or even a day or two would be acceptable.
The Bitcoin consensus rules do not require transactions to have a fee, so it's still theoretically possible for a free transaction to be confirm.

It is, however, unlikely that any miners today will confirm free transactions.  You can test this by sending yourself a free transaction to see if it confirms (but be sure you use a quality wallet, such as Bitcoin Core, that has features for handling transactions that never confirm).