I want my form to handle the arrow keys, and I can do it -- as long as there is no button on the form. Why is this?
Arrow keys are used to navigate between buttons on a form. This is standard Windows behaviour. Although you can disable this standard behaviour you should think twice before going against the platform standard. Arrow keys are meant for navigation.
If you want to get the full low down on how a key press finds its way through the message loop I recommend reading A Key's Odyssey. If you want to intercept the key press before it becomes a navigation key, you need to do so in IsKeyMsg or earlier. For example, Sertac's answer gives one such possibility.