Most ancient coins were round, but far from all. Ancient cнιɴᴇsᴇ coins for example came in different shapes, and in Japan people used rectangular coins as well as round coins with a hole in the middle.
When and where the first coins were invented is still a matter of debate, but the first coins used as a method of payment appeared around the 6th or 5th century B.C.
According to Greek historian Herotodus, first payment coins were produced in Lydia, an Iron Age kingdom in modern western Turkey. Aristotle on the other hand claimed that the first coins were minted by Demodike of Kyrme, the wife of King Midas of Phrygia.
What historians do know is that Lydians made their coins from a naturally occurring mixture of gold and silver called electrum. Lydian coins were oval-shaped and had a design on one side only. The other side was marked with simple punches.
Ancient Greeks adopted the Lydians’ method and improved it by manufacturing coins that were almost completely round coins. This technology spread throughout the ancient world.
Ancient Romans quickly discovered all benefits of round coins. For one thing, such coins could be used as an efficient propaganda tool. People who lived in the outskirts of Rome were not always well-informed about political changed in the Roman Empire.
When coins appeared with the new Emperor’s portrait, people new the previous ruler had been replaced.
Round coins were also practical because their corners could not be removed. Cutting off precious metal and trying to trade the coin’s value was very difficult.
If an dishonest money handler was tempted to snip off a bit from the edge of each coin, rendering it less valuable, he would have problems. A round coin would reveal that sort of tampering better than any other shape, since it would have a flat edge where it was snipped.
So, producing round coins was a way of preventing fraud. If you are interested in the long history of money, Ancient Pages published a comprehensive article on the subject: Our Lives Have Always Been Manipulated By Money – Part 1 – 3
In the above mentioned article, we go back 4500 years in time and find that silver rods were the world’s first money. They were introduced in Mesopotamia. It was believed they would smooth the progress of trade.