My math teacher in highschool did this. I thought he was ripping up my paper and it freaked me out.
But it looked neat and when he saw me freaking out he unfolded it and showed me the papers, hardly damaged. Then he reassembled it with the same nicks. Ta daa!

Papers joined without staple or paperclip.

Excellent photos by theinfonaut

Step 1: Get Your Poop in a Group

Gather your papers and tap the edges to line the sheets up.
Printers (the old meaning: people who print) call this "jogging".

Step 2: Fold, Spindle and Mutilate

Fold the corner over, make two small rips as shown, and fold over the resulting flap.
It's suprisingly secure and strong. You can unfold it, remove individual sheets, and put it back together quickly and easily.