can I use my date format YYYY-MM-DD ?
This date format is partially supported which means - you can type a due date using this format and it will be accepted, however after saving the task, the date will not be displayed in this format.
You're welcome to vote for the request to fully support it in our Votebox: http://todoist.com/Vote/showProposal/168/
It is a year later, and this would still be a nice (and relatively simple to implement) feature.
Maybe there aren't too many people who use YYYY-MM-DD format, but we tend to be pretty passionate about it. It is objectively the most sensible format after all ;)
Seriously though, the currently supported formats MM-DD-YYYY and DD-MM-YYYY can be ambiguous. YYYY-MM-DD is clear. It also naturally sorts properly as text, which doesn't matter here, but is a reason it should be widely used.