I never thought about source-controlling data. Isn't that what history logs are for? (I'm a developer, not a DBA, so it's probably not as simple as I'm making it sound.) In cases where a task requires some manual altering of data, I do record the script that I used in our change tracking tool, but I don't bother putting it under source control if it's just a one-and-done.
I've always been satisfied with versioning metadata changes by versioning their DDL scripts. In the case of altering an existing code module, the ALTER script can also serve as the migration script. For table structure changes, though, I prefer versioning the CREATE scripts, not the ALTER migration scripts, because then history comparisons will highlight the changes in their full context.
I never thought about using GIT for this. We don't use that for anything else on our team, so I doubt I can get my co-workers into it, but thanks for provoking that thought.