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Jimi's answer works well to stop flickering, but I don't have a good feeling about capturing mouse on mouse move. For example one issue that I see in that solution, is if you set the capture on mouse move, then keyboard shortcuts like Alt + F4 or Alt + Space will stop working.

I'd prefer to handle WndProc and set the cursor when received WM_SETCURSOR :

using System.Windows.Forms;
public class ExRichTextBox : RichTextBox
    const int WM_SETCURSOR = 0x0020;
    protected override void WndProc(ref Message m)
        if (m.Msg == WM_SETCURSOR)
            Cursor.Current = this.Cursor;
            base.WndProc(ref m);
It stops flickering. Not a perfect solution, but at least those important shortcuts will continue working.
                Well, from my experience in StackOverflow, you are one of the best WinForms experts on this site (which probably means that you are one of the bests in the world). So I believe in your ability to help the WinForms community with this REALLY important question. :D
– Michael Haddad
                Feb 8, 2019 at 11:02
                Yes, this is why I do not change the accepted answer. Jimi's answer works just fine for me.
– Michael Haddad
                Feb 8, 2019 at 11:05
                No need to change at all, unless a perfect answer is shared. I also didn't meant to affect the other answer and the other answer has my vote as well. Just shared another alternative. Specially in case some one wants to have Alt+F4 working even when the mouse is over richtextbox.
– Reza Aghaei
                Feb 8, 2019 at 11:08
I'm assuming this is the WinForms' RichTextBox, because the WPF one doesn't have this problem.
The RichTextBox handles WM_SETCURSOR messages, to change the Cursor to Cursors.Hand if the Mouse Pointer ends up on a Link. A note from the developers:
RichTextBox uses the WM_SETCURSOR message over links to allow us to
change the cursor to a hand. It does this through a synchronous
notification message. So we have to pass the message to the DefWndProc
first, and then, if we receive a notification message in the meantime
(indicated by changing "LinkCursor", we set it to a hand. Otherwise,
we call the WM_SETCURSOR implementation on Control to set it to the
user's selection for the RichTextBox's cursor.
You could set the Capture when the Mouse enters the Control's bounds and then release it when the Mouse Pointer leaves the area. The capture needs to be released otherwise, when you first click on another control, the cursor will be set to RichTextBox instead:
private void richTextBox1_MouseMove(object sender, MouseEventArgs e)
    if (!richTextBox1.ClientRectangle.Contains(e.Location)) {
        richTextBox1.Capture = false;
    else if (!richTextBox1.Capture) {
        richTextBox1.Capture = true;
                I have noticed something. When I hover the mouse over the edges of the RichTextBox, the IBeam sometimes appear again for a fraction of a second. Perhaps it's negligible for some people, but it drives me crazy. :D I have tried to capture my screen to show it, but it is so fast that even with 60fps I don't manage to capture it...
– Michael Haddad
                Feb 8, 2019 at 10:28
                The reason why you need to release the Capture is explained in the answer. See also what Reza Aghaei wrote. The Capture needs to be released when the Mouse pointer leaves the Control's area, otherwise it generates some mis-behaviours. This is also explained. If you decide to use a Custom Control, see also this: How to justify text in a label. Among the other things, there's a custom RichTextBox that supports Block Align (also known as Full justification). Maybe you have some use for it.
– Jimi
                Feb 8, 2019 at 11:01
                @Jimi My comment about capturing is, while you are release the capture when the mouse is outside the control, but when the mouse is over richtextbox, Alt+F4 will not work, because richtextbox has the capture. It's not about releasing capture when mouse leaves.
– Reza Aghaei
                Feb 8, 2019 at 11:15
                @Reza Aghaei  Yes, I know what you meant. My comment was about enforcing the need to release the capture, because the OP was apparently deciding to use just richTextBox1.Capture = true; in the event handler.
– Jimi
                Feb 8, 2019 at 11:18
        
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