The Romans used an 8-day week called the nundinum. On the 8th day of the week, rural laborers and farmers would stop work, come to the city and sell their produce. It had, or at least developed, many of the features of the modern weekend - for example, children did not go to school and most forms of work ceased.

Since this was the only time many people from the rural hinterland would ever make it to Rome, these market days were often used for making public announcements. With the passage of the lex Hortensia in 287 BC, it became formally illegal to hold meetings of the plebian assembly on market days. Certain laws accounted for the nundinal cycle; for example, one had to introduce some bills into the assembly three nundinae before they were voted on.

Ancient sources tell us that care was always taken to make sure that a market day would never fall on the first day of the year, or on the nones (either the 5th or 7th day of the month, depending which month it was), although the reasons for this are disputed. It may have been religious, because the nones of a month was not believed to be protected by any god. Similarly, when a man called Lepidus rebelled against Rome, one (not contemporary) ancient source blamed it on having allowed a market day to fall on the first day of the year, making the year unlucky.

There is debate about when the 7-day week was adopted, but references to the nundinum are very sparse after the Julio-Claudian period. The 7-day week was formally adopted for lawful use by Constantine in AD 321.

For an overview of this and a lot more, see:
Ker, James (2010), "Nundinae: The Culture of the Roman Week", Phoenix, Vol. 64, No. 3, Classical Association of Canada, pp. 360–385.