The only interesting ones I've had have been down to a captured city-state's location on the map. Playing Inland Sea and liberating a coastal city-state with navy was kinda cool. Once I had Valletta sort of behind my territory in early-game and I was really looking forward to having them as my suzerain, liberating them felt good. But often the city-state emergencies are a case of "can't be bothered to send my units all the way over there." I've had a couple of religious emergencies declared against me after converting a holy city, nothing's ever happened about it. I think one time it was only Arabia participating - and they had no cities left with their own religion. I would be quite fine if emergencies were never introduced. Most of the time it feels that a) not enough participants and not enough happening about the emergency and b) too easy and big rewards to be had.