Sure, pizza boxes are cardboard and, yes, cardboard should be recycled. But - and it's an important but - pizza boxes almost always are stained with grease and cheese and these two "contaminants" wreak havoc with the cardboard recycling process.
The best thing to do is to is to tear out the soiled parts of the pizza box and toss them in the trash. Then you can recycle the rest of the clean cardboard knowing that your efforts will help reduce the waste stream and provide material that can be processed into "new" paper products.
So enjoy your pizza! But remember - only recycle the clean cardboard from the box!