Since nobody has given a detailed response for my country's system, and I work in healthcare, I'll do my best to summarise.
AustraliaSystem: Universal public healthcare for all citizens and residents with private healthcare optional but encouraged
GDP Cost: 9.8% ($154B AU) 2013-2014
Tax Cost: 1.5% personal income tax levy (+1% for high income earners without private insurance)
SummaryIf you're poor, you can get free healthcare,
eventually. Any Emergency Room visit will be fully paid for at a public hospital. Private hospitals or mixed public/private hospitals exist that are funded by private health insurance. Elective or non-urgent surgical procedures can be accessed through public healthcare but will typically incur a waiting time running months or years depending on the type of procedure.
For non-emergency healthcare, you visit a general practitioner, a doctor who caters to simple or chronic diseases in a local business area. These are typically first point of call for general illnesses, small injuries, or prescribing of medication. A GP can either choose to accept the standard rate paid for by public health care for your visit, meaning you pay nothing, or can charge an additional cost, meaning you pay the difference between the public rate and the doctor's fee. Some GPs will also be fully private cost, meaning you pay the full amount, though these are fairly rare.
For more complex healthcare, your GP will refer you to a specialist, a doctor who focuses on one type of disease management. Examples include psychiatrists, cardiologists or endocrinologists. Not all specialist treatments are publicly funded. For example, dental treatments are typically fully private cost treatments unless delivered from a public hospital (and waiting times are usually extreme for these types of treatments). Additionally, specialists are commonly known to charge a premium on top of the standard public rate, unlike many GPs.
Finally, there's the cost of medications. The Pharmaceutical Benefits Scheme offers subsidised access to a large list of medication treatments for subsidised costs. The cost to the patient is typically capped at about $40 AU per month for each medication, with those on disability or low income receiving theirs for a little over $5 per month per medication. The remainder of the cost of the medication is paid by the Pharmaceutical Benefits Scheme. There are of course exclusions and limitations, but overall this allows equitable access to affordable medications for the majority of patients.
Those playing at home may note that the cost of all this public healthcare is far more than the amount charged in tax to fund it. Sustainability is a constant talking point and various policies get tried every election cycle to try to reduce this expenditure, but overall it's unlikely to change significantly aside from gradual erosion of benefits by exclusion.