If by worst shutout you mean the biggest shutout, then it would be the 19-0 game won by the Edmonton Oilers against the Montreal Canadiens in the 1985-1986 season.
Yes. Jose Theodore did it.
Georges Vezina in the 1912-1913 season
No
yes
Jiri Crha played 54 games in the 1980-1981 season without recording a shutout, and has a total NHL streak (over multiple seasons) of 69 games. Eldon Reddick has the longest streak without a shutout (132 games) but never played more than 48 games in a single season.
No. Martin Brodeur's first NHL game was against the Boston Bruins in the 1991-92 season. The Devils did win with the final score being 4-2, but it was not a shutout.
Abviously Martin Brodeur leades in shutouts. Even though he was injured, he has had two shutouts already. His most recent shutout was his 100 career shutout.
The Columbus Blue Jackets were shutout 16 times in the 2006-2007 season. They were even shutout twice by the Nashville Predators in just 6 days.
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Tonight? (it's April 7 2009) Carolina Huricanes beat New York Islanders 9-0
For a 9 inning game the most number of hits is 14 by the New York Giants who were shutout by the Chicago Cubs 7-0 on September 14, 1913 and the Cleveland Indians who were shutout by the Washington Nationals 9-0 on July 10, 1928.