I dug through my archive of data and found that Apple mostly keeps tabs on my interactions with the App Store and iTunes. It has a list of every single app, song, book, music video and in-app purchase I've made on my Apple devices dating all the way back to 2010. There's also a log of every time those apps were updated.
It also knows all of the songs I ever stored in iTunes Match, the service that lets you keep a cloud copy of your personal music files wherever you go.
There's even a copy of every product that I've purchased from Apple, dating to an iPhone 5, including serial numbers for all of those products. Apple also has a log of every customer support query I've made, ranging from cracked screens to questions about iPhone activation. When repairs were made, it has a log of what was damaged and serial numbers for the old and replacement parts that were added.
Aside from purchases, Apple doesn't seem to know much else. The company's privacy response team, which you need to contact in order to download the file, explains why:
"We have not included information contained within your account, if any, such as calendar contents, email contents, iTunes content etc. If you use iCloud you will note that we have extremely short retention periods for how long we store such data and we have provided all data that was available to us at the time at which we processed your request on our systems. I would also like to highlight the following from our message on Customer Privacy at http://www.apple.com/apples-commitment-to-customer-privacy: For example, conversations which take place over iMessage and FaceTime are protected by end-to-end encryption so no one but the sender and receiver can see or read them. Apple cannot decrypt that data. Similarly, we do not store data related to customers' location, Map searches or Siri requests in any identifiable form.