I haven't had to do this myself, thankfully, but some folks seem to have had success using their infrared paint remover, which basically liquifies the gunk in order to scrape it off. The tool is pricey at $300 but rental is also possible.

The original tile looks worth it! Good luck!

Here is a link that might be useful: silent paint remover review

Mineral spirtits, a plastic scraper like a windshield ice scraper, and a lot of towels.

Thanks for the feedback. :)

floorguy: Do you think these are ceramic tiles? Will the tile then need to be regrouted and resealed?

Get down there are try and scrape one with a sharp implement. If they are not ceramic, you will be able to easily cut or gouge the tile.

I am in the same boat. peel-and-stick tiles over linoleum (the pretty kind, similar to today's marmoleum). I was worried that any product I used to remove the adhesive would also etch the linoleum. I tried the real milk paint co.'s citrus solvent. Not only did it strip the adhesive without damaging the linoleum underneath, but it's safer than mineral spirits or paint thinner, the other things I was going to try if it didn't work. It's basically just orange oil. Pleasant smell, no noxious fumes. I still have to take care that the rags don't spontaneously combust, but I am very happy to have an easy solution.

I’m just about to do the same did anything work?

I just removed old vinyl tile adhesive from bathroom tiles like these. My tiles ended up being unglazed porcelain tiles from the mid 1950's. I used a wallpaper steamer to heat up and liquify the adhesive. I then scraped as much of it off with a razor blade scraper followed by scrubbing with some steel wool to get the glue out of the grout lines. Finally I wiped up the residue with a clean rag. It took me about 3 to 4 hours to do my 5ft x5ft bathroom. I also tried acetone and steel wool as a removal technique and it worked pretty well too, but ultimately I went with the steamer as it seemed less expensive and less hazardous than soaking the whole floor in acefone