The following applies to SharePoint 2007, 2010, 2013 and SharePoint Online / Office 365.
There's never an end of things to learn about SharePoint security! (I've got about 235 pages of what I've learned in SharePoint® 2010 Security for the Site Owner!) Did you know that a user without the Delete permission cannot rename files in a document library! Attempts to change the Name property of a file without having the Delete Items permission will display “Access Denied”.