I use it on my private site. Nothing fancy, just a couple of static pages. I use it for including header and footer.

PHP is totally overkill, and even a site generator feels overkill for this purpose; now I can just throw together some html and upload, no need for running a script.

Also it's a bit of nostalgia (the reason I implemented it a cople of years ago) since ssi was my first contact with web development back in '96 or whenever :)