Oh, there are several programs which generate such files, for instance some flatbed scanners. Also amongst Adobe Photoshop® professionals, for some reason multilayer TIFF is the format to go with (don't know why -- maybe because it is still popular in DTP/printing?)

Exactly, TIFF is very popular because of the printing process. You don't need layers for that of course and under normal circumstances you'd export your layered file to a one-layer TIFF.

Not really something any sane person would use GIMP for, but multi-layer GeoTIFF files are fairly common. GeoTIFF is just a TIFF file where the tags are used to store geospatial reference data. So you can have one layer contain elevation data for an area (TIFF supports floats as pixel values), one layer with aerial photography of that area, another layer with aerial photography from a thermal camera, etc.

Subtitling industry. 20 years ago. I seem to remember handling TIFF files for oriental scripts.

This is correct. Not sure if still true nowadays but even 10 years ago you could find Asian subtitles in TIFF formats on some DVDs.

I sometimes see them being used as an archive format, where PDF's are converted to tiff beforehand. Each page on a separate layer.