Only two - Mikael Samuelsson and Aaron Rome. Mikael won the 2008-2009 Stanley Cup when he was a member of the Detroit Red Wings and Aaron won it when he was a member of the Anaheim Ducks. He didn't play a game in the Stanley Cup Final so his name wasn't engraved on the Cup. However, they did include him on the Stanley Cup winning photo and gave him a Stanley Cup ring.
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The Vancouver Millionares won one in 1914, but that doesn't really count. The Vancouver Canucks have sadly won none. They went to the final game three times: first against the New York Islander then against the New York Rangers and also against the Boston Bruins in 2011 but lost all three times.