Cysts on ovaries are very common. If you have large ones they'll probably want to keep an eye on them during the pregnancy, which is what happened to me - I had to have various scans to determine what kind of cyst they were and to check they weren't growing significantly. There were some concerns that the cysts could prevent the baby's head engaging when it came to the birth, but when it came to it I had no problems. I had two big cysts of about 6cm and 10cm in diameter.
I had one when I was having ds1. I had a couple of extra scans and if for any reason I'd needed a section they would have removed it at the same time. Sometimes they go after pregnancy but mine didn't so it was removed when ds was six months old.
In both my successful pregnancies, I have had a cyst on the ovary that released the egg - in my case this was a corpus luteum cyst. In my first pregnancy, it caused a few episodes of severe pain, which resulted in me being scanned at 6 weeks. It grew to about 7cm diameter by the 12 week scan, but had gone by 20 weeks. In my current pregnancy, the cyst was seen at an 8 week scan, and again at 12 weeks, but had gone by 20 weeks again. No pain from it this time around.