I have Outlook 2013 on my PC connected to my Hotmail account using Exchange Activesync. I also have an iPhone 5 running iOS 8.0.2, connected to the same Hotmail mailbox using Exchange Activesync.
If I delete a message from my Inbox in Outlook and then look at the contents of my mailbox in the Webmail interface, the message has been deleted there too. However, if I then look at my mailbox on the iPhone, the message hasn't been deleted, so I have to delete it manually there a second time. New mail arrives fine on the iPhone, so it's working in that respect. It's just message deletion that seems not to sync.
This problem isn't an iOS 8 specific thing, it's been going on for a very long time in iOS 7 too. Possibly longer.
I've deleted the mail account and readded several times, to no avail.
What could the problem be? It's drivin' me crraaaazzyyyy!