The "day of rest" on Sunday derives from Judaisim and does not make its way into Roman practice until the time of Constantine. Romans of the Republic and Early Empire worked every day and had no concept of the "week."

But, never fear. There were nearly 200 Roman festival days (feriae), when a lot of people would be "off" work. Many people were living hand to mouth, earning the money for food the day they ate it, and of course a "day off" for them was probably pretty rare. But for the rest, there enough fun days to more than make up for the lack of weekends. A quick, non-comprehensive list:

January - festival of Janus; Compitalia; Carmentalia

February - Parentalia/Feralia; Lupercalia; horse races!

March - Mars holiday; Liberalia; more horse races

April - Venus holiday; Megalesia (Cybele); Ceres holiday; Parilia; flower holiday; many others

May - Lares festival; festival to the dead

June - Vestalia; holidays for Jupiter, Juno, Mars, Minerva, etc.

July - Apollo holidays; Concordia holiday; Neptunalia; Fortuna

August - ten or more holidays to various deities; fun month

September - Jupiter holidays; Capitoline triad; Venus Genetrix

October - Capitoline games to Jupiter; Juno, Ceres, and others

November - 14 days for the Plebeian games/feast

December - Saturnalia; numerous other holidays (another really fun month)