Toilet plunging 101. Allow the bowl to fill. Lower the plunger into the water vertically to catch the air. Seat the snout of the plunger into the discharge area of the bowl. With one smooth motion, push down forcefully, and stop. Remove the plunger and repeat if necessary. Insider tip, the plungers which have a bell shaped top and a tapering lower portion seal better, and plunge more effectively. Too many folk just annoy the water in the bowl owing to ineffective technique. Trust me-when you do property maintenance for absentee landlords, and have day-care centers as clients, you obtain your PhD in potties.
Go to Home Depot and look for the most dangerous stuff you can find. Usually the bottles are themselves wrapped in a second plastic bag and there’s warning lables all over it. It’s close to pure sulfuric acid and will make short work of a few paper towels.
Uh… this is a bad idea. If you were to actually read all the no-nos on a bottle of industrial strength drain cleaner, you’d see that “do not put this stuff down a toilet” is prominently displayed. Try plunging the toilet properly (danceswithcats uses my method), if that doesn’t help, try the wire-clothes-hanger method discribed by Cillasi. If your only problem is really paper towels, then some combination of these two procedures should take care of it. And, please, leave the sulfuric acid on the shelf.
Get a toilet auger. They are available in 3 foot or 6 foot lengths, and cost anywhere from $10 (cheap 3 foot) to $50 (good 6 foot). It’s the same idea as a coat hanger, but it is designed for the job. It has a foot that is padded so it won’t scratch the toilet bowl, and a handle on the top so you can turn it easily. Here are some: http://www.plumbingstore.com/toiletaugers.html