Pizza boxes have been determined to not be recyclable because of the grease, tomato paste, and cheese that is usually smeared all over the thing. If this is the case DO NOT recycle your pizza box. However, some pizzas come with a cardboard insert that in essence protects the box from the pizza ooze. In this case, throw away the pizza ooze protector disk and recycle the NON-SOILED box. Similarly, you can tear out the soiled segments of cardboard to be disposed of in the trash while recycling the portions that are free from grease, cheese, and other pizza associated flotsam.
If you are having trouble determining the degree to which your pizza box is soiled, do not recycle it. You can end up doing more bad than good when the cardboard is recycled into other materials. If you still loath the idea of throwing away soiled cardboard, you have another option. You can compost that box as "brown" material!