The Hibernian Football Club of Edinburgh, Scotland, Who Last Won The Scottish Cup In 1902 And Have A Longer Championship Drought Than The 1908 World Series Winners, The Chicago Cubs

Here's what you need to know about sports droughts, here's a nice little history of the Hibernian Football Club, here's their official site (this page shows that 1902 victory), and yes, you can order stuff from their souvenir shop.