Some writers and publications, such as The New Yorker, use ö in English words such as zoölogy and coöperate to indicate diaresis, i.e. that the second vowel is pronounced separately. However, it's far more common to write zoology, cooperate, etc. It is also employed in names such as Laocoön, Coös County, and the constellation Boötes.
It is also used in some German loanwords, such as ?