Don't worry, I'm really not THAT easily offended. :) It's just that such a term is not really used by anyone.
Most of Eastern Europe including parts of the former USSR these days don't look all that different from USA. People are poorer no doubt, but not to such an extent that it's obvious. Most people drive older cars out of necessity instead of choice, I guess would be the most visible sign.
It was never really about economics, when the phrase was coined. The First World were the countries allied with the USA, regardless of per-capita income. The second world was the Communist Bloc. The Third World was everybody who didn't fall into one camp or the other : The Non-Aligned Nations. It just so happened that that was composed mostly of poor, ex-colonial nations. Not entirely, though: Switzerland, Austria, Sweden and Finland were all considered members of the Third World, given their official neutrality. Which seems bizzare, given that the phrase has now become synonymous with poverty and underdevelopment, but there you go. Words are a funny thing.
From the original context, I suppose you could say there's still a 'second world' : North Korea, Vietnam, and Cuba. (After the Sino-Soviet split, China was counted as part of the Third World. Not for its level of development, again, but because of its status vis-a-vis the superpowers.) Pretty small world, though.