What browser are you using, have you tried a different browser to see if it works.
I use Chrome and drag and drop works without problem.
You can also move emails to folder by ticking the box on the left of the email list then go to the menu bar at the top of the list of emails and click on the "more" button. This will give you a drop down box. Click on "move to" and another box will open with a lost of your folder. Select the folder you want and click on it. The email should then be moved.
You can move more than one email at a time by ticking the left hand box for all the emails that you want moved to the same folder.
