Jean Beliveau has won 17 Stanley Cups. (10 as player, 7 as executive)
Henri Richard has won 11 Stanley Cups, all as a player.
The Montreal Canadiens have won the most Stanley Cups with 24.
The Montreal Canadiens have won the most Stanley Cups, as of 2014.
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Mike Gartner, Luke Richardson and Harry Howell played well over 1400 games without winning a Cup. Many have played over 1000 games without winning. However, these guys at least made the playoffs once in a while. The most unusual is probably Guy Charron who played 734 regular season games with Montreal, Kansas City, Detroit and Washington and not only never won a Cup but never once made the playoffs.