Dennis Bergkamp
One of the finest strikers to have come from the goldmine of talent that is the Netherlands, he too has never won the Champions League. Having played for Ajax, Inter Milan and Arsenal, his biggest achievement in European competition was winning the UEFA Cup twice (with Ajax and Inter). In 11 seasons with Arsenal, he has won the Premier League thrice and the FA Cup four times. He was also an integral part of the Invincibles team that went an entire season unbeaten (2003-04) in a run that stretched to 49 games.
But when it came to the Champions League, the Gunners were never a real threat and always fell in the knockout stages of the competition. The closest he came to winning it was in 2006 when they lost in the final to Barcelona. But he was on the bench in what was to be his final game for Arsenal. A Champions League trophy would have been the best way to sign off for the Non-Flying Dutchman.