Single sign-on authentication systems such as OAuth 2.0 are widely used in web services. They allow users to use accounts registered with major identity providers such as Google and Facebook to login on multiple services (relying parties). These services can both identify users and access a subset of the user's data stored with the provider. We empirically investigate the end-user privacy implications of OAuth 2.0 implementations in relying parties most visited around the world. We collect data on the use of OAuth-based logins in the Alexa Top 500 sites per country for five countries. We categorize user data made available by four identity providers (Google, Facebook, Apple and LinkedIn) and evaluate popular services accessing user data from the SSO platforms of these providers. Many services allow users to choose from multiple login options (with different identity providers). Our results reveal that services request different categories and amounts of personal data from different providers, with at least one choice undeniably more privacy-intrusive. These privacy choices (and their privacy implications) are highly invisible to users. Based on our analysis, we also identify areas which could improve user privacy and help users make informed decisions.