I'll go first

- Internet and Email... that's pretty much a given I guess. Can include everything from browsing to shopping to banking.
- Importing Pictures from Cameras.
- Editing, and when needed, printing Pictures.
- General housekeeping (system backup and general file backup/sync)
- Programming, not something I do much anymore due to difficulty typing (there's loads of ways to get started programming with Linux, Python is a good place to start, IMO).
- Scanning/Printing etc. Linux supports all of my scanners and printers, and most printing is done wirelessly over the network.
- Letter writing, shopping lists, keeping track of rent and other finances (Libre Office handles all that)
- Running Virtual Machines (Virtualbox). I've not found viable alternatives to iTunes and Samsung Kies, so I run them in Windows VMs - the VMs don't have network/internet access.
- Video encoding/editing. Some of the TV episodes I get need re-encoding before they are watchable on standalone players - wildlife videos I make need editing (for my own use, nothing fancy).
- Burning various video to DVD.
- Editing playlists for mp3 player.