I've been very lucky, this happened on my first cruise on the Splendour.
We're in a outside cabin on desk 2, sailing into the Strait of Gibraltar, I opened the curtains and swimming past the window was a lone dolphin. One of those double take moments. Later in the cruise, a transatlantic one, I looked down from the Spa and watched a sea turtle causally swim past.
MikeTheKid's post reminded me of a good story...While on AOS in port, my wife had just gotten out of the shower and was totally naked. I had the curtains to the balcony wide open. We heard a funny "Bell" sound a few times, but it didn't register what it meant. A few moments later, two maitenence workers were on a scaffolding outside our window waving at us. My wife shreiked and immediately hit the floor while I almost choked on my coffee in laughter. That was several years ago and she still talks about it like it was yesterday.