I've just re-discovered it - I don't like re-discovering things. I have spent an hour trying to solve this problem and once I've figured out how to do it, I've realized that I had had exactly the same problem about a month ago and I had already worked it out back then.
Anyway, let's describe the problem first:
1. There is a form - myForm.
2. There is a TextBox (or RichTextBox) control on myForm - myText. There is also a Button - myButton - on the same form.
3. The AcceptButton property of myForm is set to myButton.
4. The myText.Multiline is set to true. However, pressing Enter key does not insert a newline, but activates myButton instead.
The solution is simple:
1. In myText.GotFocus (or myText.Enter) event set myForm.AcceptButton to Nothing (VB) or null (C#).
2. In myText.LostFocus (or myText.Leave) event set myForm.AcceptButton back to myButton.