I think the French system works quite well (although they're talking about changing it which I'm not happy about).
There's basic social coverage for everyone. This is free (well, paid for by taxes) and covers all essential, health stuff (including antibiotics etc.)
Then there's the "top-up" health insurance, which covers most things not covered by the state. Often your contract is through your work (you usually can't opt out of this) and payment is taken at source.
When you go to the Dr you pay upfront (23 euros usually). This used to be fully reimbursed but recently they changed it for "solidarity" so you get 21 euros back.
Treatment is sometimes paid for upfront (and then reimbursed by social coverage and/or the top-up), sometimes you don't pay anything upfront and it's fully covered (e.g. for all my pregnancy stuff I never paid anything upfront).
They've also now introduced a "solidarity" tax for medicine - mostly it'll reimbursed except for 50 cents per product - this is to try and reduce the amount of medicines people claim for! (a nation of hypochondriacs)
For people without a lot of money (means tested):
Either the top-up health insurance is completely free, or you get a voucher contributing to it, so you get a 50, 60 or 70% discount etc.
I like the system because I never have to wait for an appointment. At most, I've had to wait one day to see a Dr. (specialists can usually be seen within a week or 2, with one exception who had a waiting list of 6 months but he's very good
).
There's also an SOS Dr system with a Dr making house calls. At most I've waited 3 hours for one. Yes I had to pay 50 euros for his visit but I got it all back.