I looked at my phone this morning and there were no new emails on my Hotmail tile. I thought that was unusual so figuring the notification on the tile was broken I went ahead and opened it. There are no emails at all showing in Hotmail - not even old ones. I resynced and still nothing. No errors are coming up. By going to the Hotmail web site I verified I still have all my emails including new ones. I launched Live Mail on my desktop and the new emails came through there. I assume it'll all be fixed by removing the mail account and adding it again, but I figured I would post this to see if others have had a similar experience.
EDIT:I just tried sending an email from the phone and it went out fine, but it does not show up in the sent folder.
Ditto here, just happened to me. It was fine this morning but now on the phone, no emails - the folder structure is still there, but folders which were set to sync now show the "sync this folder" as an option as if it were new. Choosing that doesn't bring any email down, though. Verified both through outlook and hotmail.com that the account is active and working, so seems like the phone sync is the only problem.
What if you don't have a Twitter account? My wife's Lumia 900 has since yesterday the same problem. She has only the Hotmail account connected to her phone, nothing else. The weird thing is that there is not error message and it worked for several months without problems (and still works on my phone).