1987 Toronto Blue Jays
11 years into their existence as a franchise, the Toronto Blue Jays were a good team that never seemed able to make it over the hump. The 1987 season looked like it would be their year. All the Blue Jays had to do was pick up one win against the Detroit Tigers and they would've been in the playoffs. But that didn't happen. Detroit swept the series and sent the Blue Jays home to cry into their denim and apologize politely to their fans until hockey season started.