Manchester City and Sheffield United became the first two clubs to draw as many 18 of their games in a single Premier League campaign. Both clubs accomplished this during the 1993-94 season. This was when each team played 42 games.
The following season Southampton matched their record by drawing 18 games in 1994-95.
Since the Premier League was reduced to 20 teams from 1995-96, the following teams have drawn 17 games during a 38-game season:
Newcastle United (2003-04)
Aston Villa (2006-07 & 2011-12)