Human civilization spans over thousands of years and several great civilizations rose and just vanished as if they never existed. History records great empires to have existed in China, Egypt, Mesopotamia (present day Iraq), Persia, India, etc. that stretched far and wide and were considered to be great in their own respect. Now, each of the above mentioned countries were more like nation states which cannot be called countries because today the term country denoted something different than what was prevalent then.
These countries were ruled by several kings over the years and encompassed most of the present day boundaries. The names of these regions are mentioned in historical documents that date back to several thousand years. Did you know that San Marino has the oldest written constitution (1600 A.D.), that is in effect even today?
Mesopotamia literally means 'the land that lies between rivers' i.e. the Tigris and Euphrates. The history or Mesopotemia can be traced as far back as 5300 BC when urban societies of Ubaid period prospered. This place also called cradle of civilization has seen Bronze and Iron Age. With the march of time, it has also seen the rise and all of Sumer and the Akkadian, Babylonian and Assyrian, Neo-Assyrian and Neo-Babylonian empires during the Bronze Age. Since the fall of Babylon in 539 BC to the Achaemenid Empire, it was conquered by Alexander the Great (in 332 BC), the Sassanid Persians (AD 226). It was in the 7th century that it fell to Arab Islamic conquest and came to be known as Iraq.
It was Pharaoh Narmer who is credited with unification of upper and lower regions of present day Egypt in 3100 BC. There were several conquests and subsequent change of regimes in ancient Egypt, and later due to a series of events led to the British conquering large parts of the country. Over the years, the people of Egypt struggled for freedom and eventually, on February 28, 1922, the country was declared independent.
The rise of the Van Lang tribe in 2879 BC led to the formation of Vietnam as a single country. Regime change continued over the centuries and was later ruled by the Japanese rulers, who later left the country after the Second World War on September 2, 1945.
Korean Peninsula - 2333 BC
Historical records say that it was in 2333 BC that Korea was founded By King Dangum. In the latter centuries the country was divided and reunified several times, besides being invaded by the Russians and Mongols. The Japanese ruled the country from 1910 till the end of the Second World War, after which Korea was divided into two different countries - North Korea and South Korea.
One of the oldest countries in the world, China was first founded by Xia Dynasty and it was in 221 BC that the Qin Dynasty unified most parts of present day China and it was only in 1949 that the Republic of China came into existence in its current form.
The country was unified for the first time in 337 BC under King Philip II of Macedon. The modern-day republican form of government in Greece was formed in 1821.
Majority of the Indian subcontinent comprising most parts of present day India, Pakistan and Bangladesh was unified by Emperor Chandragupta Maurya of the Maurya Dynasty in 322 BC. The next several centuries saw several dynasties come and go, and the last rulers of present day India, Pakistan and Bangladesh were the British, before India and Pakistan (Bangladesh was included as a part of Pakistan) gained independence in 1947 and later declared republic.
Thus, there is no definite answer to the question which is the oldest country in the world. One must also remember that there are quite a few countries which date back to the days long before Christ was born, if we consider their present day political boundaries.