Less spectacular than the brilliant ideas above, but connected to daily life:
Make biodiesel from palm oil. Saponify, separate, esterify, separate. Ask someone else for the details. You can replace dangerous methanol with a bigger alcohol.
Or simpler: make soap from grease or oil.
Or make biodiesel from soap. Fewer steps.
Distill "crude oil" to white spirit, Diesel oil and lubricants. You previously mix the "crude oil" from this commercial ware. Have a fire extinguisher at hand.
Distill resin into turpentine and rosin.
Bleach coloured molecules with some oxidizer: hypochlorite, percarbonate, hydrogen peroxide... against varied dyes, natural and artificial, organic and not.
Pyrolyse "plastic waste" to fuels. Be absolutely sure your plastic is a polyolefine (one single part, floats on water, burns with candle odour. Then make chips of it), since others emit toxic gases.
Experiment around flash points. Try to ignite gasoline, Diesel oil, turpentine, wax... at room temperature and at heat, or with a wick.
Make a polymer. Polyamids are easy.
Make a glue from an elastomer or polymer in a solvent.