We present an in-depth study of co-following on Twitter based on the observation that two Twitter users whose followers have similar friends are also similar, even though they might not share any direct links or a single mutual follower. We show how this observation contributes to (i) a better understanding of language-agnostic user classification on Twitter, (ii) eliciting opportunities for Computational Social Science, and (iii) improving online marketing by identifying cross-selling opportunities. We start with a machine learning problem of predicting a user's preference among two alternative choices of Twitter friends. We show that co-following information provides strong signals for diverse classification tasks and that these signals persist even when (i) the most discriminative features are removed and (ii) only relatively "sparse" users with fewer than 152 but more than 43 Twitter friends are considered. Going beyond mere classification performance optimization, we present applications of our methodology to Computational Social Science. Here we confirm stereotypes such as that the country singer Kenny Chesney (@kennychesney) is more popular among @GOP followers, whereas Lady Gaga (@ladygaga) enjoys more support from @TheDemocrats followers. In the domain of marketing we give evidence that celebrity endorsement is reflected in co-following and we demonstrate how our methodology can be used to reveal the audience similarities between Apple and Puma and, less obviously, between Nike and Coca-Cola. Concerning a user's popularity we find a statistically significant connection between having a more "average" followership and having more followers than direct rivals. Interestingly, a \emph{larger} audience also seems to be linked to a \emph{less diverse} audience in terms of their co-following.