I’ve just read a nice example of why hyphenating adjectives consisting of multiple words matters in English. Consider the following sentence:
He became the third world champion.
and compare it to this:
He became the third-world champion.
Quite a bit of difference, isn’t it? Of course, the rules for using the hyphen are somewhat more complicated than that; you can read more on the topic in my article about the hyphen, minus, en-dash, and em-dash.