Really, the premise of the movies. A sociopathic Knight Templar with a messy moral philosophy is forcing people to mutilate themselves as a form of "rehabilitation" or else they die... and that's because said sociopath believes they're wasting their lives in immorality without suffering for it. Now, if you happen to have done any of the things that got characters in the films killed (which include self-harming, drugs, alcohol abuse, getting a divorce, taking antidepressants, being even slightly unfaithful to your partner, lying about your health, and more) and then are foolish enough to watch the movies, good luck sleeping. You'll be checking your closets for people in pig masks for weeks.
Billy the Puppet. Granted, he looks pretty inconspicuous on and doesn't really do anything other than deliver messages, but just look at this thing. He looks like a twisted cross between a ventriloquist dummy and a harlequin with bright, angry red eyes and even appears to be moving on his own in some scenes. And that's before he starts speaking with Jigsaw's raspy mechanical voice to deliver a cruel take-down of you, and you realize he might be the last face you ever see before you meet an incredibly gruesome demise.
Meta example: Those traps are terrifying by themselves. What's more terrifying is that someone in the real world had to make sure they are somewhat plausible.
Most (if not all) of the traps are based on actual torture or death devices. Screenwriter Leigh Whannell described it as "only scratching the surface of how horrible human beings have been to one another for all eternity."
Also in the second game is Solomon, whose trap has him tied to a rack and placed over burners on a track. Michael has to push him around, solving the puzzles that unlock the gates to move on all while keeping him off of the burners that are spewing flames. Imagine being in that man's shoes: having to trust someone to keep you moving forwards out of the danger of being cooked alive, all while there's a fire igniting under you...