#4 Rangers
Scottish giants Rangers FC might be in doldrums at this point in time and playing in the second division in Scotland, but they remain the most successful club in the country's history.
Rangers have won the league 54 times, which is a record for any club anywhere in the world. In addition to that, they have won the Scottish Cup (33) and the Scottish League Cup (27), 60 times in total.
However, success in the continent has eluded them and they have nothing to show for their efforts since 1972, when they became the first club from Britain to win a European trophy in the form of the Cup Winners' Cup.
Other than that, Rangers have never really threatened in the Champions League, despite their pedigree as one of the world's biggest clubs. They ended as the finalists of the UEFA Cup back in 2008 and in addition to that, they had two runners-up finishes in the Cup Winners' Cup in 1961 and then again in 1967.
They are, without a doubt, one of the biggest underachievers in European competitions among big clubs.