If you are employed your employer pays for it. If you are unemployed the job centre will pay for it. If you are self employed I believe you pay about 120€ a month. So unless you're self employed you don't pay for anything.
This year they scrapped the 10€ every three months but last year you would pay that at the doctor and that would cover you at that doctor and a female doctor if you needed one. You'd also pay 10€ at the dentist. If you're on a low income you get a card which you show which makes you exempt.
This year I had gallbladder surgery and I had to pay 110€ towards it (the whole thing cost 4000€ I had so many tests done) but because I'm on a low income I didn't have to. If I was earning enough I wouldn't have minded paying for it as I only had to wait two days for the operation and the aftercare was top notch. I only had to pay 20€ towards the cost of my pregnancy. I had several scans (Germans firmly believe more scans are better and Germany has a rather low stillbirth rate - 4th lowest in Europe I believe), a free 3D scan and loads more. The insurance also paid for a family midwife to visit me twice a week and help me out with this like shopping, baby groups etc and all I paid was 20€.
So yeah, right now the 10€ every three months isn't applicable and your employer/job centre pay for main insurance. Some things you don't have to contribute to but when you do it's not much.
I'd rather pay for an excellent service than get a not so good one for free.
Yeah, Germany has an awesome healthcare system. Can't complain at all. Well, eye care can be costly as well as dental care. Overall a top system though. 8% of everyone's monthly pay goes toward health insurance and it's taken straight out of the paycheck so you wouldn't have even known it was ever there. I like that much better than being responsible for covering yourself. Too iffy for me.
By the way, how were you able to get all those midwife visits? I wish I would have known about all that when I was pregnant with my first. I had no idea about all the help available!