If everything else mentioned here fails and you are specifying a Outlook Web server URL as the Exchange server in iOS, i.e., outlookweb.domain.com, check the number of devices you have registered with the Outlook Web server. Unknown to most of us, there is a limit of 10 mobile phones a user can sync with an Outlook Web server. If you try to register the 11th, you will get an email from "Outlook" addressed to your Exchange email address that says:
Subject: Error with your new mobile phone partnership
You have 10 phone partnerships out of the maximum allowed 10 partnerships. After you reach the maximum, you can't create additional partnerships until you delete existing ones from your account. To do so, sign in to Outlook Web App, click Options > Phone > Mobile Phones, and delete any unused partnerships.
Check your junk mail since it may have ended up in there. If you did get it, you have to drill down through "more options" in Outlook Web to find the Phone menu. Once I deleted my old devices, I was able to sync with no problems. BTW, if you have more than one iPhone/iPad registered, you can highlight each one and click on "details" to figure out which is which since they are all listed as just iPhone/iPad.
My thanks to scrateef on the MacRumors iOS8 forum for this information.