On 16 September 1979, the Serie A season kicked off with eight matches, seven of which ended in draws.
Goals were at a premium that day, as eleven of the sixteen teams in action failed to find the net, resulting in five scoreless draws: Ascoli-Napoli, Avellino-Lazio, Cagliari-Torino, Perugia-Catanzaro, and Roma-Milan. The other ineffective attack came from Pescara, who were on the wrong end of the day's only unbalanced result, losing 2-0 to Inter.
There were also two score draws, both of which ended 1-1: Fiorentina-Udinese and Juventus-Bologna.
Other leagues have experienced similar days, with eight draws out of eleven English First Division matches on 10 September 1966 and eight draws out of ten matches in the thirteenth round of the Argentine Clausura (though the matches occurred over a period of three days). On a percentage basis, the record goes to Scotland, with draws in all six Premier Division matches played on 22 January 1994.
[Special thanks to the Guardian's John Ashdown for the information, published in his Knowledge column on 3 May 2011.]