Open return tickets have faded away but they still exist in some airlines.
Here are few links from prominent airlines about open return tickets
British Airways: contact sales office on telephone to enquire about open return tickets.
British Airways Questions And Answers
KLM - book fully flexible ticket - refer to first response provided by KLM:
Turkish Airlines - open return tickets are issued - seems like through contact centers - refer to question 4 and 5
AeroFlot airlines: contact sales office - premium business class ticket
Qantas airlines - open return tickets are not allowed
Qantas Booking An Open-Dated Ticket
One will have to call up the customer service department of the airline one wants to travel with to check whether they have the option of open return or not. Almost all airlines nowadays have Fully flexible, semi-flexible ticketing options which allows the traveler to change/modify the flights which might come at some cost and rules differ from airline to airline.
Open return tickets are not completely out of the door but it seems that most airlines have at least started showing it the exit door. At least I have encountered or found any airline who allows us to see prices for open return flights online and I am pretty certain they would cost a fortune to book nowadays.
The closest option to open return tickets are semi-flexible and fully flexible type options with airlines but one needs to be careful as there is a lot of fine print (different for each airline) which one needs to be aware of before actually making the booking.
