It has methods like CRichEditCtrl::Copy(), CRichEditCtrl::Paste() which you can call, but I can\'t spot any messages the control is sent by Windows
What happens when the user requests a paste action is usually that a WM_COMMAND message with the identifier ID_EDIT_PASTE is sent to the rich edit control. By default in MFC this is handled by CRichEditCtrl::OnEditPaste(), which calls Paste() on the edit control itself.
The way I'd go about this is to derive a class from CRichEditCtrl, add an OnEditPaste method and route the message to it with a
ON_COMMAND(ID_EDIT_PASTE, OnEditPaste)
declaration, which should work. Alternatively, in your PreTranslateMessage you could look for WM_COMMAND with a wParam of ID_EDIT_PASTE.
By the way, I've solved a very similar problem to yours (paste without formatting) by just having an implementation of OnEditPaste with
void MyRichEdit::OnEditPaste()
{
SendMessage(EM_PASTESPECIAL,CF_UNICODETEXT);
}
This responds to the paste request by sending a paste message to the control that insists that the data format is plain text.
Finally, I should point out that the above technique is sufficient to catch all pastes triggered from the user interface. However, it won't catch programmatically triggered pastes, when your code sends WM_PASTE to the edit control. In those cases it's easiest to just change your code. However, if you really want to intercept such cases, you have to get your hands dirty with COM and IRichEditOleCallback::QueryAcceptData. But you almost certainly don't want to go there :-)