A complete search of the internet has found these results:
pieces of paper is the most popular phrase on the web.
"pieces of paper" is much more commonly used, but "pieces of papers" could be used when there are multiple pieces or bits of paper from mulitple different papers.
7,303,221 results on the web
I'm sure a couple pieces of paper are fine.
Really. I mean, these are just pieces of paper.
I spent some quality time with some meaningless pieces of paper.
And there are a bunch of Teen Wolf related words and phrases written on pieces of paper in that thing.
Torn up pieces of paper in his wallet.
And... some pieces of paper.
Those aren't just two pieces of paper in your billfold.
Three round pieces of paper taped to his shirt.
Look at those pieces of paper just sitting on my desk.
The winning tickets are just pieces of paper now.
That's just pieces of paper.
This whole country is founded on these three pieces of paper.
Luke, inside this box is a pencil and two pieces of paper.
67,003 results on the web
A few pieces of papers on my father's desk blew onto the floor.
Really. I mean, these are just pieces of papers I used to keep underneath my bed.
The pieces of the papers I wrote for school were scattered across my floor--the dog ate my homework!
She has torn-up pieces of papers she sent to her boyfriend in her pocket still.
Some pieces of the papers the author wrote are still in circulation.
Pieces of the papers tattooed into the minds of the teenagers attending.
The mailman picked up pieces of papers he had just dropped.
Pieces of papers torn off of flyers littered the city in the morning.