There were two great related articles in The New York Times last month concerning recycling:
In the latter article they specifically address the subject of pizza boxes as one of the six:
Pizza boxes are among the most common offenders when it comes to
contamination, waste managers say. The problem is that oil often seeps
into the cardboard. The oil cannot be separated from the fiber, making
that material less valuable, and less marketable, to buyers.
But that’s not to say you can never recycle a pizza box, said Marjorie
Griek, executive director of the National Recycling Coalition, which
promotes recycling in the United States. “If you’ve got a few crumbs
in there, that’s not an issue,” she said.
Pizza boxes with “small amounts of grease” are O.K. to recycle in New
York City, a sanitation department spokeswoman said. If the grease
seeps through the cardboard, the box should be put in a composting bin
or thrown out, she said.
Remember, there are also two sides to a pizza box. If there’s a side
that’s not oily, tear that off and recycle it.
The other thing I loved about this article is that it introduced to me the phrase/concept of "aspirational recycling"... that is the act of recycling items that you hope will be recyclable. In many cases items flowing into the recycling stream that not truly recyclable may result in the entire batch being discarded (this topic is covered in depth in the former article).
The conclusion being that you really need to know if greasy pizza boxes are recyclable in your area. If you are just acting on your hope they are you may be doing much more harm than good.