The main ferry connections between Greece and Turkey are Rhodes-Marmaris, Rhodes-Fethiye, Kos-Bodrum, Rhodes-Bodrum, Samos-Kusadasi, Chios-Cesme and Lesvos-Ayvalik. 
These lines are all - except Samos-Kusadasi - operated whole year round.  In winter (November 1st - March 31st), mainly twice a week, in Summer (April 1st - October 31st) almost daily by either the Greek or Turkish ferry company.  And in the peak season (mid-June to mid-September), you may even have two connections a day.
For these lines, you have the option to take a one-way ticket, an open return ticket or a daily return (except for Lesvos-Ayvalik).
Greek port taxes only apply for the open return tickets.  Turkish port taxes are applied for all tickets.  The amount of the taxes vary depending the embarkation port.