If you're speaking in terms of big-picture, geopolitical alignment as /u/Gerry-Mandarin suggests, then no: the three "world" system as we know it today is a product of the Cold War.
If you're talking about "developing countries" then the answer is "sort of." Since the development of agriculture, and especially agriculture intensive enough to allow the creation of cities something like 4000 BCE--give or take a few centuries--then there have been portions of the world where the environment is more intensively used and managed than in others, and in which there are greater concentrations of people, typically with a more diverse range of skills and often with more complex political organizations like states. These regions have also tended to expand over time since then, although not continuously and not without some substantial contractions. Be careful not to assume that these more "developed" regions and their societies are "ahead" of others; human history is not a race and "development" is at its most basic the level the manner in which each society finds ways to meet its needs through interaction with its environment.
We might with some reservations call these regions "core" areas, with denser populations and more intensive land uses, while areas with thinner populations and less intensive (or more extensive) land uses are "peripheries". Some fundamental changes have occurred between core and periphery regions beginning perhaps as far back as Song China about 1000 CE, with its greater commercialization, perhaps more recently with the creation of the Atlantic world after 1500, with its reorientation of land, labor, and commerce in the Americas, Africa, and Europe. Really fundamental changes have intensified since the 19th century with European imperialism. The major change is the core regions have become more effective at dominating peripheries through the extension and projection of political power. Core regions from the 19th century on have been able to dictate how peripheries use their land and resources, directing the "development" of peripheries along lines that benefited the core. This includes, for example, constructing sugar or cotton plantations in Latin America and the US South, "development" that provided raw materials for the core regions of western Europe and the NE United States, and which generally allowed the core regions to accumulate capital while the peripheries more or less stagnated. This core-periphery relationship is roughly the north-south divide we see in global wealth today, and in this view, the Cold War and its division of the world into three "worlds" can be seen as two different factions from the global north, the "core" regions of the world, competing for influence over the third world, the global periphery.
Not really. Or probably not in the sense of what you're thinking of. Third World does not denote poverty. Ireland, Austria and Switzerland were Third World countries whilst Iran was First World. The term is purely related to the Cold War to divide the world into "us", "them" and "everybody else".
The First World was the US led group of themselves, occupied Japan, western Europe, and white Dominions of the Commonwealth (plus other leftover territories of the UK).
The Second World was the USSR led group of eastern Europe, Cuba and much of Asia, extending into many post-colonial nations.
The Third World were neutral countries.
Now, whilst I can't think of any "ancient" forms of this kind of relationship. I can think of a precursor situation between the UK and the Russian Empire during the 19th Century (briefly revived in the 20th), known as the Great Game.
Much like the US and USSR conflicted over territory primarily in south east Asia (and their economic methods), the UK and Russia conflicted over territory in central Asia (but for colonies in the traditional sense). In this sense, the UK, its colonies, allies (and their colonies) would be a "First World", Russia, and its colonies as the "Second World", with the rest of the world as the "Third World".