Buffalo Sabres: founded in 1970; never won a Stanley Cup

Franchises that existed in 1970 and haven’t won the Stanley Cup after 1970 (with last win if applicable): Toronto Maple Leafs (1966), Chicago Black Hawks (1960), Los Angeles Kings, St. Louis Blues, Vancouver Canucks, Buffalo Sabres

Existing franchises that haven’t won the Stanley Cup (with years founded): Los Angeles Kings (1967), St. Louis Blues (1967), Vancouver Canucks (1970), Buffalo Sabres (1970), Washington Capitals (1974), Winnipeg Jets/Phoenix Coyotes (1979), San Jose Sharks (1991), Ottawa Senators (1992), Florida Panthers (1993), Nashville Predators (1998), Atlanta Thrashers (1999), Columbus Blue Jackets (2000), Minnesota Wild (2000)

More info: Wikipedia