In Australia, you have a mix of public and private health. Everyone gets Medicare (the public health system), but you pay a Medicare levy if you earn over a certain amount. This is usually 1.5% tax on your income. You get benefits and 'rewards' if you opt to take out private medical insurance, like subsided premiums. You;re also encouraged to take out insurance sooner in life, as your premiums when you first take out insurance increase with age, and continue at a higher rate.
I pay for private insurance for my entire family - myself, wife, and two sons.
I recently had an operation, and went private. I was charged for the initial consultation with the specialist, then the procedure itself (general and local anaesthetic, then surgery).
Total out of pocket expense to me was AU$300. $140 for the consultation (not covered by our insurance), and $160 'gap' for the operation, so the cost not covered by insurance. If I'd gone public, I would have waited a few more weeks, but it would have cost me nothing.