As of 2017 is it still possible to get a transaction confirmed without a fee?
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).