Yes, the odds are greatly in one's favor. In my 30 cruises, I can remember only one instance that was major. Ironically, it also happened to be our favorite cruise! It was Celebrity Century in 2007 -- there was a leaky pipe somewhere that ended up soaking our rug and everything on it. In addition to the apologies, the staff cleaned all of our laundry (that had been sitting in a laundry bag on the rug) and even cleaned the suitcases that were under our bed! Additionally, they gave us a second cabin in which to change into our formal wear that evening, and to spend the night if we had wanted.
I'm sure there were other instances -- I just don't remember them, or the memory fades with time.