Instant messaging services are quickly becoming the most dominant form of communication among consumers around the world. Apple iMessage, for example, handles over 2 billion message each day, while WhatsApp claims 16 billion messages from 400 million international users. To protect user privacy, these services typically implement end-to-end and transport layer encryption, which are meant to make eavesdropping infeasible even for the service providers themselves. In this paper, however, we show that it is possible for an eavesdropper to learn information about user actions, the language of messages, and even the length of those messages with greater than 96% accuracy despite the use of state-of-the-art encryption technologies simply by observing the sizes of encrypted packet. While our evaluation focuses on Apple iMessage, the attacks are completely generic and we show how they can be applied to many popular messaging services, including WhatsApp, Viber, and Telegram.