There may not be a pure keyboard shortcut to do it (actually, there is — Oz ed), but Mac OS X does allow copying and pasting of files—by using the mouse and the Option key. Normally, the default system behaviour would just move a file that's dragged by the mouse, but doing this will cause it to make a copy of the file, just as though you had used the copy/paste functions in an app.
There's a situation when the default behaviour is reversed, though. OS X will try to copy files being dragged by mouse between drives, such as in a network situation. For those instances, you can hold down the Command key while dragging the file. You'll notice that the "plus" icon will disappear, meaning it's not copying, and the file will be moved from the drive it's on to the new drive.