Relative to what, the US? I'd say the thirty wealthiest countries on the planet... except us.

Norway

Since we are talking about the cold war: USSR.

They had pretty good results post WW2. The problem is that they ended up lagging behind the western bloc because of a lack of resources and innovation. Basic healthcare doesn't mean much if you don't have good treatment in the first place. It is a common problem with communist countries, they usually have good access to healthcare, but they don't have the resources to give proper treatment.

China