There aren't any airlines that offer official open-ended tickets however airlines that have the option to buy more expensive airfares such as business class and first class, provide passengers with greater flexibility than an economy ticket would.
At Alternative Airlines we ticket over 650 airlines for you to choose from, each one including the option for Cancellation Protection.
How long are open tickets valid for?
The general rule for open-ended tickets was that the return flight had to be purchased and redeemed within 12 months of the outbound flight. Some tickets opted for a 1 month's return and some for longer at 36 months.