None have. It isn't possible according to NHL rules. The Tampa Bay Lightning tried to in 2010 but were disqualified for trying to do so.
Carolina Hurricanes
yes last spring the sixth seeded LA kings won the 2014 Stanley cup.
once
7 Teams have won the Stanley Cup since the Presidents trophy was incorporated in the NHL in 1976.
The 2011 Los Angeles Kings won the Stanley Cup as a last place #8 seed
Yes! The Vancouver Millionaires won the Stanley Cup in 1915. The Vancouver Canucks have not yet won a Stanley Cup.
The Montreal Canadiens won the 1946 Stanley Cup.
The Victoria Cougars won the Stanley Cup in 1925.
The Toronto Maple Leafs won the 1932 Stanley Cup.
The Toronto Maple Leafs won the 1962 Stanley Cup.
The Seattle Metropolitians won the Stanley Cup in the 1916-17 series.
The Boston Bruins won the Stanley cup in the 2010-2011 Stanley Cup finals against the Vancouver Canucks