The St. Louis Blues have won 138 playoff games and have never won a Stanley Cup. They've also PLAYED the most playoff games - 307 - without winning a Cup. The San Jose Sharks have played the most playoff games - 136 - and won the most - 64 - without even MAKING it to the final series. Of the NHL's 30 teams, 13 have never won a Cup, and 6 have never played in a final series. All that information comes from the NHL Guide and Record Book, issued every autumn and available in bookstores near you.
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 1947 Stanley Cup.
The Toronto Maple Leafs won the 1962 Stanley Cup.
The Toronto Maple Leafs won the 1932 Stanley Cup.