They have never won the Premier League.
Arsenal have won the Barclay's premier league 3 times
Wigan Athletic have never won the Premier League.
Chelsea has won the FA Cup seven times. It has also won the premier league four times. The premier league is the most competitive league in England.
Liverpool has won the premier league eighteen times.
since it was called the premier league arsenal have won it 4 times but in total wining it when it was called league 1 and premier league thet have won it 20 times
Fulham have never won the Premier League.
Manchester United have won the Premier League 13 times.
As of the end of the 2014/2015 Premier League, Burnley have never won it.
As of the end of the 2014/2015 Premier League, Swansea have never won it.
Man Utd have won the English league (first division) 7 times, not including the English Premier League, which the have won 11 times.