#2 Damon Hill

The British driver won the world championship in the year 1996. He and Nico Rosberg are the only two champions who are the sons of former world champions (Damon Hill being the son of Graham Hill).
Graham Hill won the Monaco Grand Prix 5 times, but his son failed to score a victory even once. All throughout the '90s and his Championship years, Hill was equipped with a fast Williams car but, unfortunately, bad luck prevented him to win at Monaco.
He finished 2nd in 1993 and 1995 but, the closest he came was in 1996. Hill dominated almost throughout the entire race, but sadly due to an engine failure, he had to retire out of the race.
#1 Nelson Piquet

Piquet is probably the most successful F1 drivers who has never won the Monaco Grand Prix. During his hugely successful career, he managed to become a triple world champion (1981, 1983, 1987).
The Brazillian has 23 wins to his name and 60 podium finishes. He started the Monaco GP 12 times, and failed to win it even once. He came closest in 1981, when he led the race for 58 laps, but spun out at the last moment.
Piquet was never good at Monaco and always qualified quite low in the grid. It could be because of Alain Prost and Ayrton Senna, during the time, who dominated at Monaco, winning the race 10 times.