Another, closely related, case is when you love the culture the language gives you access to. Learning a language without interesting books/movies/tv shows behind it will most probably be a chore.
The first sentence is important. It's not about the abstract idea of "interesting items of culture" existing. IME they have to be already interesting to the learner to be a motivating factor.
Some people likely find any items of culture interesting. I'm not one of those people, and I suspect most around me aren't either, or we'd all know a lot more languages.
Personally, I like Spanish as a language and am learning it, and as a result I find that I have access to more Spanish movies/shows/books because I understand it better. It wasn't my goal, but it's a welcome perk, and my comment was mostly about the fact that even if you don't learn a language for it's culture, there's always a culture there for you to enjoy once you do.