I saw this post which made me wonder just what the numbering system means now:
http://boards.straightdope.com/sdmb/showpost.php?p=15288160&postcount=40
Ok second world? 
And yes I know that the numbering originated in the cold war, but it seems to have taken on a life of its own.
I think of the second world as countries that have large segments of the populace that are reasonably comfortable, but still have large pockets of poor and/or lots of dysfunction in their institutions: countries that are either on their way up to first world status, or on their way down to third world status.
The classification is a Cold War relic - “first world” was the western democracies (and a few outliers like Japan), “second world” were the communists, and “third world” was everyone else. I’m not sure how it applies today.
It’s definitely a cold war relic, but coincidentally the world could be considered to be in three economic tiers. You have developed and developing countries, then you have a third set that are pretty much stagnant; maybe even worse off in real terms than they were 30 years ago.
This is not to lay (more) criticism on the countries / failed states that find themselves in the last tier; it’s to highlight that the simple developed / developing classification hides some of the reality.
I suppose the second world would still include Cuba and North Korea.
Dont forget the fourth world: tribal people unaffiliated with national borders or non participant societies embedded within others.
There are even a couple of unclaimed territories in the world, though it is because they are largely inhospitable, or politics. Politics what? Exactly.
Example: Bir Tawil
Historically, the First World included the industrial capitalist democracies of North America and western Europe, plus Japan, Australia, and a few others in which economic levels were high and industry was well developed.
The Second World, rarely referenced, were the industrial communist countries including the USSR and its Eastern European satellites. They had high industrial development, but a different economic model. It usually did not include non-industrial communist countries like mainland China.
The Third World was used to refer to all the countries outside of these two groups, mostly with an agrarian economy and a low level of industrial development, regardless of the economic system. It included capitalist countries like Brazil and India as well as communist countries like mainland China.
Today these groupings are obsolete. However, “First World” is still used for developed countries, and “Third World” for those that are underdeveloped. There are no remaining countries that fit the original definition of Second World, since existent communist countries are either severely underdeveloped like Cuba and North Korea, or aren’t really following a communist economic model like China.
“Fourth World” is sometimes used to refer to countries that are not merely underdeveloped, but stagnant or moving backward like Somalia and Afghanistan.