If you want to drag from your list view to the desktop, call DoDragDrop and create a new DataObject in the format of a FileDrop. You will need to create a temporary file to set as the file you would like to copy.
string MyFilePath = @"C:\Documents and Settings\All Users\Temp\TempFile.txt";
listView.DoDragDrop(new DataObject(DataFormats.FileDrop, MyFilePath) , DragDropEffects.Copy);
This will take the path of the temp file that you will have created and create a File Drop object, so that the desktop can recognise it and allow the copy.