Some slightly scary stories here but just to reassure that in my own research on the subject I have not heard of a bad outcome for either mother or baby, including people who have had operations to remove cysts during pregnancy.
2 x 5cm and 1 x 7 cm cysts were found on one of my ovaries at my first scan (and somewhat concerning my other ovary hasn't been located at all!).
I've been told that they will not do anything (operating is really the only option) unless the cause any further problems (eg rupture or twist). They do not seem overly concerned and cysts in general are not at all uncommon in pregnancy and do normally resolve without causing further problems.
With the benefit of hindsight I think I have experienced ruptured cysts twice before I was pregnant. And I can confirm yes it is painful - it felt being shot in the stomach and was in bed for three days. I didn't see a doctor as I thought it was severe period pain at the time!
My consultant has not said anything about rupture being more risky during pregnancy but I will ask at my next appointment.
And although general anaesthetics aren't carried out on a whim during pregnancy, many women have to have them for various reasons and again I have not heard of a bad outcome.
So although it is another thing at the back of my mind to worry about I am not overly concerned - my biggest fear (given one ovary AWOL and another with multiple cysts) is future fertility but will cross that bridge when we come to it