Runoff voting is quite common, and is used all around us.
In 1996, the Ontario Liberal Party held a leadership convention. Hundreds of delegates had to choose between seven candidates. When they counted all the votes, a man named Gerrard Kennedy had the most votes. Trailing far behind, in fourth place, was a fellow named Dalton McGuinty. If they were using Toronto's election system, the race would have been over. But no one had a majority of the votes, so they proceeded to have a series of "runoff" votes, with the least popular candidate removed on each round. Dalton McGuinty was declared the winner on the fifth ballot because he was able to build the broadest level of support from the voters.
All of Canada's parties, and all of Ontario's parties use runoff voting to choose their leaders. They also use runoff voting to nominate their candidates in every riding, in every election.
In the McGuinty example, they were using a "multi-round" model, where participants had to vote five times. With a ranked ballot, they only would have voted once.
Over the last decade, all of our federal parties have implemented use of a ranked ballot. This allows all members to vote (in advance) not just those attending the convention.
How popular are ranked ballots? In 2010, even the Academy Awards adopted ranked ballots to choose Best Picture! This was done to avoid a situation where a movie could "win" with only 20% support in the Academy. The NHL and NBA also use ranked ballots for their awards.
Cities all across the USA use runoff voting to elect their mayor and/or city council. Recently, many of those cities (including San Francisco and Minneapolis) have modified their system, switching to a ranked ballot and an instant runoff (full list here).