I think it depends a lot on climate. For me the models I associated with them at first were oxfords and especially the tie loafers. They have a great range and I have rarely seen a model that I wouldn't have in my feet given unlimited spending power. That versatility might be what's iconic about them (as well as the price point).
I share the seem experience. My first two purchases was the single monk split toe loafer (I thought at first that model was one of their iconic models) and the string loafers. Rubi red shell also comes to Mind and the double monks on the inca last. Also if cold weather like Roger said the jumper boots.