My favourite plague is when the AI decides to punish you endlessly by spreading it back and forth to your cities. Two infected AI spies entered one of my cities, then four or five turns later, moved into a neighbouring settlement and infected that. Then, just as the first city has recovered, it moves its plaguebearers back to that city, then keeps going back and forth to each one just when they are recovering. Despite having 6-10 spies and assassins (many 5 star or more) in each settlement, I couldn't stop the AI spies murdering my population for a period of 30 years or more. I even tried surrounding my cities with agents to stop the AI spies entering but to no avail. Finally, after 10,000 deaths or more, I killed the plague-bearing spies.

The next best plague is when you accidently infect your best fleet with the plague. For fleets, there is no cure that I recall, only death.