Update: An update in the course of 2014 rendered this obsolete.
Exchange email, calendars and tasks work well enough with iOS devices (iPad and iPhone) but not OS X.
Google revealed the usual spread of despairing cries for help followed by suggestions of varying usefulness. A couple of top tips include the news that, when there is no field to enter your domain, you can specify your username as <domain>\<username>. This is apparently well-known to Windows system administrators (although why anyone would do that job voluntarily remains a mystery to me).
This did not solve the problem. Nor did confirming the port number and all the other settings which work on iOS.
If your mobile devices work fine with your Exchange accounts but your OS X computers do not, despite apparently using all the right settings, ask your Exchange administrator if EWS is configured and how.
Finally, I would like to take this opportunity to ask Microsoft’s public affairs team not to get in touch. Open, non-proprietary protocols are available and your dreadful software, which has brought untold low-level misery to millions, should use them.