If you understand what your client is ultimately wanting to achieving, you will see (much of) the scope creep before they do.

When you start thinking that you're smarter than your client, and that you can know what they want before they do, you're on very dangerous ground. You may be right much of the time, but when you're wrong you can find yourself down a deep hole.

If you do not really understand what they ultimately want out of the project, then you don't know whether they really understand what they want.

You avoid this trap by showing your client working software at frequent intervals, and by asking "Is this right? Is this what you meant?", letting them clarify, change their minds, let you know about new requirements, or smile and nod. You both gain understanding and trust incrementally.

Scott Ambler has a talk titled Are You Agile, or Are You Fragile that touches on this problem.