Considering that they run Sound of Music tours in Salzburg, and that anniversaries of the film's debut are marked by television specials, we'd say that love and fandom for the film run pretty deep.
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Since 2000, a sing-along version of the film toured Britain. With audiences dressed in lederhosen or nuns' habits, the film is screened with subtitled dialogue so you can sing your heart out and know all the words (as if you didn't already). As the film's 50th anniversary approached, the sing-along became a worldwide phenomenon.
Things can get pretty raucous.
The biggest fans were probably that generation of kids growing up in the '60s who, with their parents, watched the VHS of The Sound of Music endlessly and returned to see it in theaters over and over. In some towns, the number of tickets sold far exceeded the population of the town, suggesting that there were a lot of repeat viewings. One woman in Wales even claimed to have seen it 900 times (source).
In fact, the only place in the world where the film wasn't wildly popular was Germany and Austria. Germans and Austrians still aren't fans; they didn't like filmmakers messing with their true stories. And we're assuming there's that whole Nazi thing they'd like to forget…