It's not copying an empty block, it's copying the blank line. You can change this setting in Tools > Options > Text Editor > All Languages > 'Apply Cut or Copy Commands to blank lines when there is no selection'
I'm using Visual Studio 2008 (but I believe this answer applies to Visual Studio 2005).
Select Tools -> Options.
Navigate to the "Text Editor" node and expand it.
Expand "All Languages" (or whatever language you want to apply this to) and check the "Apply Cut or Copy commands to blank lines when there is no selection".
The option that saved my sanity is found in Tools - Options - Text Editor - All Languages - General. There's a checkbox Apply Cut or Copy commands to blank lines when there is no selection. Unchecking this allowed me to hit Ctrl+C all i want on a blank line without losing the content on my clipboard.