Of course, for some of the bigger sides in the country, the potential for a David vs Goliath outcome is less about romanticism, and more of a humiliating banana skin that must be avoided.
Historically, some clubs have been more prone to bowing out at the hands of a minnow than others, and Leeds United have fallen victim on more than one occasion.
As recently as 2018 they were knocked out by League Two outfit Newport County, and the year before that they were undone by non-league Sutton United.
This season could prove to be just as dangerous too, with a clash against Crawley Town to contend with on Sunday. The Reds are unbeaten in their last five matches, and currently sixth in the fourth tier.
But where do the Whites rank in terms of other giants who have been slain throughout the years?
BetVictor have taken the difference in league positions between every top side and the teams who have knocked them out over the past 25 years, and have come up with a cumulative total for each club.
Click and scroll through the pages below to see the top 10, and to see how Leeds measure up compared to some of the most illustrious teams in the country: