What's the most creative or unconventional use of Git you've encountered?

I use it to backup my save games. Not sure if that's conventional.
For example, I'd MKLink %appdata%/Local/Pal/Save/ to a folder in my save repo, and commit that every once in a while.
- Fun story, in 2012 I got the idea of making a git based "cloud" save system with branching, to explore multiple story paths in games.
  I implemented the FileSystemWatcher (the equivalent to Linux's inotify) component in C# on Windows, was able to detect when games were saved, and commit that to git, and stopped there.
  Feel free to implement that, I'd love to save on implementation time 😇

There's a gut repo of the German constitution (Grundgesetz) with all changes with correct dates and authors:
https://github.com/c3e/grundgesetz
And it exists for all laws in Germany, too: https://bundestag.github.io/gesetze/
Created/funded by a government sponsored fund for open source software
- I wish all rules, Ts&Cs, contracts, etc came like this. It might make it less unfeasible to follow what's changed when something forces you to agree to the new version of the terms.

I wanted to automate the setup of my desktop environment, but didn't know what got changed in the individual config files when I tweaked a setting in the UI.
So, I did a git init in ~/.config/, added all files to an initial commit, and then made the change in the UI. Afterwards, a git diff showed the exact changes I wanted.

I used it once for version controlling my master's when I was writing it. I wrote it in Markdown with Pandoc syntax, so it worked. I eventually gave up and just used LibreOffice, though, since it was a hassle
- I worked with LaTeX a lot, but none of my collaborators used git. They just dump the files in dropbox. Still nice to use git just for yourself so you can view changes easily.
- Was it the version controlling or writing in markdown part that was a hassle?
  
  Both lol. The reason is that I had to render it to DOCX each time for my PI to review it, because she was an old retrograde woman. Therefore, rendering the document, committing changes and reading Git and Pandoc documentation took time -- the time that I could've used to write the actual thing

Tracking season-by-season changes to my fantasy football league's charter.
Business logic mermaid diagrams installed as a submodule in every projects repo.

I've put ASTs directly into git repositories by encoding each leaf as a blob and each tree as a tree. Since git objects are content-addressed, this gives deduplication of ASTs for free, including CSE for sufficiently-pure ASTs.

ifc-git.
ifc is an iso standard for 3d construction projects, which includes all aspects of a building data. because ifc is in human-readable form, versions of the same project can be diffed, hence ifc git.
this is a really underappreciated project.

I tried to take hourly snapshots of an already-large Minecraft world using Git, but after a few years of snapshots, the repository became corrupted.
One of the issues was that regardless of any player-based changes that occurred, the spawn regions were always different as they were always loaded in memory.

Not very clever or rare, but extremely useful. On my persistent Unix/Linux boxes, I "git branch /etc" as soon as it comes up. Then all of my admin config gets committed whenever it's changed.
- Have you tried etckeeper? I haven't, but it's supposed to be an improvement over just using git in this usecase.