You just need a good protective case.
My Kindle 3 lives in a Saddleback Leather medium gadget pouch. It's survived overseas trips from Australia to Bali, Vietnam, US. It's been chuck under plane seats in a bag, dragged around on trains, buses, in the basket of bicycles, on motorcycles.
No problems what so ever. Just be a bit careful like you would with any other electronic gadget.
I can't see an airport scanner being any rougher than what mine's been through and yes, perhaps take it out and put in a tray like you would your notebook.