This is not to say that you should purposely compost toxic or harmful material (battery acid is not a good idea), just that things we might usually consider harmful, like poop, come out of the composting process as pathogen free and nutrient rich materials. As always, what you compost is up to you, and may be dictated by the kind of composting system you have, but with a little creativity almost anything you have can be composted.
Now, without further delay, here is the Who Says It Can't Be Composted Compost List:
Pizza Boxes and other Soiled Paper Products:
It is a special pet peeve of mine when 'do not compost' lists include pizza boxes. These can most certainly be composted, in fact, nothing else really can be done with them as they gum up recycling machines and will ruin a whole batch of cardboard, and putting them in the garbage will just contribute to landfill produced methane, which causes the greenhouse effect, as well as wastes valuable resources, rather than recycling them back into the environment.
Cardboard pizza boxes are the most common example of soiled paper products, but used toilet paper, dirty paper towels, and any paper-based, wax coated (as opposed to plastic coated) take out containers can all be safely added to the compost bin without fear of contamination or impeding the biological breakdown process. If you happened to use a paper towel to clean up battery acid you might want to just throw it away, but anything else that would normally spoil paper products can be composted without problem; grease, oil, butter, spilled kool-aid, bits of food, and coffee soaked things can all be composted. You can even toss water-damaged novels in the compost bin (only if they're too damaged to be usable, remember, reuse before recycle), though you might want to cut it up first to facilitate quick decomposition.
Of course, before you decide to go on a paper-products buying bonanza, remember that many of these things can be replaced by reusable versions (handkerchiefs instead of tissue, towels instead of paper towels, and cleaning rags instead of old newspapers (get an online subscription instead)), which will be much cheaper in the long run and better for the planet. Still, while you're switching over, or in case you find one of these items indispensable, keep composting in mind as a viable alternative to just throwing it away. Plus, even the most hard core activists like to order a pizza once in a while.
Meat and Dairy Products:
Most people advise against composting meat and dairy products, and possibly other food scraps such as bread, eggshells, and leftover prepared food, because of the risk of attracting pests and rodents to their compost pile. As long as the pile is about one cubic yard in volume and is turned regularly, this should not be a problem. I know that one cubic yard sounds like a lot, but you can easily generate this much compost in about a month through collecting your lawn trimmings, kitchen scraps, and pruning a few trees or rosebushes. This volume of compost allows you to bury the questionable food scraps in the middle of the pile, thus making them less accessible to roaming animals. Additionally, turning the pile at least once a month keeps the environment of the pile changing which discourages rodents, who like a stable, navigational environment.
Meat and dairy products are also popular favorites on the 'do not compost' lists because of the risk of pathogens. However, as you will soon see, even the most pathogen-infested of material can be rendered safe through the miracle of composting. If you are particularly worried about it, only use the compost for horticultural application, rather than agricultural. If you aren't eating food made from the compost, then you're not ingesting any possible diseases. You eliminate the risk of pathogens by leaving the compost to sit undisturbed for a year and a half (no adding new material), as this is long enough that all disease-causing microorganisms will have died off, or by making sure that you have a large enough compost pile for thermophilic bacteria to move in and kill off the bad guys. There's a lot of things you can do to ensure a thermophilic pile, but the primary one is to have a big pile; the bigger the pile the easier it is to heat up. I know that's not a lot to go on, but thermophilic composting is a huge topic, and this post is long enough already, so look for a more detailed post on this topic at a later date.
Weeds and weed seed containing material are not typically recommended for composting because of the risk of infesting cleaner garden soil with weed-ridden compost. However, thermophilic compost piles will also take care of this problem, as that type of bacteria kills seeds as well as pathogens. However, there are other ways of composting weeds to keep them from becoming a problem in your finished compost. The first, and easiest, is just composting as usual, and then pulling any weeds that may grow in the resulting compost. Well-mulched and composted garden beds are a breeze to weed, and ripping weeds out of finished compost is even easier. However, if you have a bad weed problem, or if you're just not as lazy as I am, you can also rot the weeds down. Just put water and weeds into a container, cover it with some sort of lid, and let it sit for a week or so. The resulting mixture of rotten plant sludge will smell like death, but will also be a nutrient rich additive for your compost that has no viable weed seeds, shoots, or bits left to start any trouble at all in your compost. I recommend emptying the bucket into the middle of your compost pile just before you go to bed. Bury the concoction well to keep the smell down, and by the time you wake up the reek should be gone.
Poop, Pee, and Other Bodily Productions:
Dog and cat poo are always included on the 'do not compost' lists, and most people would never consider composting their own waste, but it's really not that hard or dangerous to do, and would actually solve a lot of our water usage and pathogen outbreak problems if we had a system-wide methods of composting waste rather than "treating" sewage. However, since this is an icky subject, and since you haven't had time to learn to love me enough to put up with the un-wonderful detail that we'll have to go into in order to fully explain humanure processing, let's just stick with pet waste composting.
Poop and cat litter can be composted as long as the pile is (say it with me) thermophilic, or allowed to sit, untouched for eighteen months. I like to make an in-ground dog poop composter (two actually), to trade off on letting materials decompose long enough to become inert. Then I mix the resulting humus in with my regular compost for a turn or two to make sure that everything is good and diverse, then I dig it into my garden. Of course, if I was worried about soil contamination, I would only use poop compost on non-food gardening projects, but I believe in the power of compost, so I don't worry about it, though some people might, and that's just fine.
On a supplementary note, cat litter should only be composted if it's biodegradable, so litter made from sawdust, corn cobs, wheat hulls, and newspapers is all okay, but clay, sand, and crystalline based litters aren't so great because they can easily leach toxins and can easily mess up your soil structure.
Body waste is not limited to things that come out the back end. Nail and hair trimmings are also things that most people might not thing about, but which can easily be composted. They can also safely be composted in a normal pile, which is more than can be said for most other things talked about here today, so if you're not comfortable with composting weeds, meat, or doodie, then at least remember your friend the planet when you're cutting your nails and ordering a pizza.