Is there any shortcut to select the current line in Visual Studio?

Clicking the line 3 times does the trick

If you want to copy a line, simply place cursor somewhere in that line and hit CTRL+C

To cut an entire line CTRL+X

@Sean found what I was looking for:

To disable this default behavior remove the checkmark (or check to re-enable)

Apply cut or copy commands to blank lines when there is no selection

Accessed from the menu bar: Tools | Options | Text Editor | All languages

You can also enter copy into the options search box for quicker access

[Tested in VS2008, 2010, 2017]