Clipboard Monitor

The problem is that you're handling the wrong window message. Quoting the documentation for AddClipboardFormatListener:

When a window has been added to the clipboard format listener list, it is posted a WM_CLIPBOARDUPDATE message whenever the contents of the clipboard have changed.

With that knowledge, change the code to:

const int WM_CLIPBOARDUPDATE = 0x031D;
protected override void WndProc(ref Message m)
{
    switch (m.Msg)
    {
        case WM_CLIPBOARDUPDATE:
            IDataObject iData = Clipboard.GetDataObject();
            if (iData.GetDataPresent(DataFormats.Text))
            {
                string data = (string)iData.GetData(DataFormats.Text);
            }
            break;


        default:
            base.WndProc(ref m);
            break;
    }
}

SharpClipboard as a library could be of more benefit as it encapsulates the same features into one fine component library. You can then access its ClipboardChanged event and detect various data-formats when they're cut/copied.

You can choose the various data-formats you want to monitor:

var clipboard = new SharpClipboard();

clipboard.ObservableFormats.Texts = true;
clipboard.ObservableFormats.Files = true;
clipboard.ObservableFormats.Images = true;
clipboard.ObservableFormats.Others = true;

Here's an example using its ClipboardChanged event:

private void ClipboardChanged(Object sender, ClipboardChangedEventArgs e)
{
    // Is the content copied of text type?
    if (e.ContentType == SharpClipboard.ContentTypes.Text)
    {
        // Get the cut/copied text.
        Debug.WriteLine(clipboard.ClipboardText);
    }

    // Is the content copied of image type?
    else if (e.ContentType == SharpClipboard.ContentTypes.Image)
    {
        // Get the cut/copied image.
        Image img = clipboard.ClipboardImage;
    }

    // Is the content copied of file type?
    else if (e.ContentType == SharpClipboard.ContentTypes.Files)
    {
        // Get the cut/copied file/files.
        Debug.WriteLine(clipboard.ClipboardFiles.ToArray());

        // ...or use 'ClipboardFile' to get a single copied file.
        Debug.WriteLine(clipboard.ClipboardFile);
    }

    // If the cut/copied content is complex, use 'Other'.
    else if (e.ContentType == SharpClipboard.ContentTypes.Other)
    {
        // Do something with 'e.Content' here...
    }
}

You can also find out the application that the cut/copy event occurred on together with its details:

private void ClipboardChanged(Object sender, SharpClipboard.ClipboardChangedEventArgs e)
{
    // Gets the application's executable name.
    Debug.WriteLine(e.SourceApplication.Name);
    // Gets the application's window title.
    Debug.WriteLine(e.SourceApplication.Title);
    // Gets the application's process ID.
    Debug.WriteLine(e.SourceApplication.ID.ToString());
    // Gets the application's executable path.
    Debug.WriteLine(e.SourceApplication.Path);
}

There are also other events such as the MonitorChanged event which listens whenever clipboard-monitoring is disabled, meaning that you can enable or disable monitoring the clipboard at runtime.

In addition to all this, since it's a component, you can use it in Designer View by dragging-and-dropping it to a Windows Form, making it super easy for anyone to customize its options and work with its inbuilt events.

SharpClipboard seems to be the very best option for clipboard-monitoring scenarios in .NET.