Civil engineering can be described1 as the profession of designing and executing structural works that serve the general public.
Civil Engineering as a separate discipline only exists as such for less than three centuries. However, one can successfully2 reason that civil engineering is a lot older than that, even if not explicitly named as such. One has only to look at the public works built by the ancient Romans to conclude that the practice of civil engineering existed long before the name for it was coined somewhere in the 18th century.

History of the practice of civil engineering

The ancients started building civil works long before our calendar was even thinking of coming into existence. A few examples:

And even after the western world was initiated to the calendar as we know it (in its first few crude forms, that is), we have quite a few examples of civil engineering prior to the 18th century:
  • Extensive irrigation system constructed by the Hohokam Indians, Salt River, AZ around 600 AD
  • First dykes defending against high water in Friesland, The Netherlands around 1000 AD
  • El Camino Real - The Royal Road, Eastern Branch, TX and Western Branch, NM (1500s AD)
  • Great Wall of China (1640 AD)
Maybe civil engineering hasn't been with the human race since its beginnings, it certainly peeked in along the bumpy road leading to where we are now since the species got beyond its diaper stage.

History of the term civil engineering

According to the online Encyclopædia Britannica the first man to call himself a civil engineer was John Smeaton, who designed the Eddystone Lighthouse (1756-59 AD) and founded the Society of Civil Engineers (now known as the Smeatonian Society) in 1771.
The encyclopædia is of course British, and the coining of the term civil engineer or civil engineering (or equivalents in other languages) is different for each country.
For example, in The Netherlands4 civil works were originally carried out by a special division of the military (called 'genie'5 in Dutch). After the Napoleontic times (-1815 AD), a civil branch of the military genie came into being and was called 'civiel' to differentiate it from its military counterpart. In France the term still is 'genie civil'.

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1 This definition is from the online Encyclopædia Britannica
2 In my opinion: unavoidably
3 Off the top of my head... correct me if I got the name wrong
4 Sorry guys, I'm Dutch...
5 From the same French word

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   Sources:
http://www.britannica.com
http://www.asce.org/history/
Dutch college manual: Inleiding Civiele Techniek (Introduction Civil Engineering) - September 1995; DUT