Here we have the ten best systems in the world according to the WHO:
1 France (two-tier, access to private health care at own expense, though leaning and very expensive at USD3,048 per person per year, or 11.2% of annual GDP)
2 Italy (two-tier, option to take out private insurance, and less expensive at USD3,314)
3 San Marino (I haven't found much info, but it appears to be single-payer, but can't be sure, and no cost estimate)
4 Andorra (two-tier, public and private insurance, no cost estimate)
5 Malta (two-tier, public and private options, no cost estimate)
6 Singapore (two-tier (perhaps the closest to the US' as far as universal access goes in terms of private invovement, but much better planned), 3% of annual GDP)
7 Spain (two-tier, similar to the UK one, no cost estimate)
8 Oman (two-tier, public and private parallel systems, no cost estimate found)
9 Austria (at least mostly single-payer, maybe two-tier, but unclear, no cost estimate)
10 Japan (two-tier, 8.2% of GDP or UDS2,908)
18 United Kingdom (two-tier allowing unrestricted private health care in conjunction with public, USD2,317)
23 Sweden (two-tier, leaning more towards single-payer, but undergoing reform as it allows more private-sector involvement, USD2,745)
30 Canada (two-tier, leaning much more towards single-payer, USD2,998)
37 United States of America (two-tier, much more privatized, not universal, and highly inefficient at USD5,711)