The previous owner of our house, unfortunately, tried to "renovate" and "improve" the recently refinished and refurbished original clear-vertical-grain fir floors by sticking self-adhesive vinyl tiles to them to create "area rugs" of faux parquet and faux marble. After scraping, heating, and using a variety of solvents, I hit upon this far easier and relatively non-toxic method: dry ice.
Step 1: Materials
30 lbs dry ice
waxed or parchment paper
hand towel or rags
small flexible putty knife
Step 2: Arrange Dry Ice
Open a few doors and windows. Consider turning the fan on. While the CO2 gas from the evaporating dry ice isn't poisonous, it is heavier than air and not usefully breathable. Small children and cats, being closer to the ground, can suffocate if the CO2 is allowed to accumulate.
Tear off a piece of waxed paper or parchment paper large enough to cover a tile and overhang an inch or two on each side.
While wearing insulating gloves, arrange the chunks of dry ice on top of the paper to cover the offending tile. Cover the ice with a towel or two to insulate it.
Wait 2-3 minutes. Read a book, like I did. Often, you can hear an audible "pop" when the tile comes loose.
Step 3: Repeat
Use the piece of paper, pulling on the edge, to reposition the dry ice to the next, more offensive, tile.
Use the scraper or putty knife to lift the previous tile. Often, you can just lift the tile up with your fingertips. Put the tile in a bag or box. If left on the floor, it will soon re-adhere itself.
Step 4: Repeat Until the Floor Is Clean
If you aren't bored enough, attack what little adhesive remains after a tile removal with the putty knife, while it is still cold.