Saw/Recap
Warning: This plot summary is written with the events of the films arranged in chronological order, rather than in the order of which film they happened in. Since the films jump back and forth chronologically, especially in the latter installments, don't think you can avoid spoilers by reading this summary and stopping when you see events that aren't familiar. Reading this will spectacularly spoiler the plot of the entire series for you; You Have Been Warned.
John Kramer was an unassuming, successful engineer who drifted through life without worry until his son was stillborn after an attack on wife Jill, a rehab clinic doctor, by one of her addict patients. If that wasn't bad enough, he was shortly afterward diagnosed with an inoperable frontal brain tumor, and his insurance company refused to fund an experimental treatment that could cure him (or at least alleviate his suffering). His death sentence filled him with bitterness at all the healthy people who take their lives and situations for granted, and one night, he attempted suicide by driving off a bridge. He survived the attempt, believing the experience had granted him clarity, and then he set out to "rehabilitate" people into appreciating their lives...by placing them into nightmarish death traps. After his "work" comes to light, the press dubs him the "Jigsaw Killer", or "Jigsaw" (for the jigsaw-shaped piece of flesh he cuts from his "patients", symbolic of the "missing piece" of their life that prevented them from being "rehabilitated").
Eventually, one of Jigsaw's victims switches over to his side: a young drug addict named Amanda, who helped Jill's attacker and managed to win her game, escaping with her life. Jigsaw gained a second apprentice in Detective Hoffman, one of the officers investigating his murders. Hoffman was so obsessed with avenging his sister's murder that he killed the perpetrator in a Jigsaw-esque death trap; Jigsaw discovered this and recruited Hoffman, threatening to expose him if he broke Jigsaw's rules. Amanda and Hoffman both created inescapable traps; Amanda did it because she considered his methods too lenient, and Hoffman did it to help cover his tracks. Eventually, Hoffman blackmails Amanda into shooting one of Jigsaw's test subjects despite being told by Jigsaw not to; this costs Amanda her life, and Jigsaw himself dies soon afterward.
Even after the death of Jigsaw, the police continued to investigate his killings. Hoffman eventually dispatched the persistent Agent Strahm and framed him as Jigsaw's second accomplice, throwing suspicion off of himself. But when the police examine new victims and unscramble Hoffman's voice tapes - delivered to them by Jill Tuck, Jigsaw's wife, as part of Jigsaw's final requests - they discover that he was the real accomplice. Hoffman kills everyone who discovers the truth and returns to oversee Jigsaw's final game (which involves the insurance agent who denied his coverage application). But Jigsaw's actual final game was to test Hoffman himself - Jill Tuck puts Hoffman in a trap without any instructions for escaping, leaving him to die. Hoffman survives the game, however, due to some quick thinking, after which Jill narrowly escapes Hoffman (who's understandably pissed off) and reports him to the police straight away, making all of Hoffman's efforts to frame Strahm worthless.
Hoffman demands (through video messages) that the police turn over Jill to him, or else the games will continue. The police don't yield, and so the ongoing game ends as poorly as ever. Meanwhile, Hoffman single-handed-ly dispatches a whole police unit and ends up confronting Jill in her cell where she was locked for safety. Hoffman puts Jill in the original Reverse Bear Trap without any means of escape, and she dies to it. Hoffman destroys his lair and believes himself to be ultimately victorious...but on the way out, he's captured by the one person no one would ever suspect - Dr. Lawrence Gordon, who has been missing since the first film. Dr. Gordon survived his trap (by sawing off his foot and cauterizing the wound as he crawled away) and became Jigsaw's real apprentice, privy to all his schemes, unlike both Hoffman and Amanda; it's also clear that Jigsaw made him Jill's protector, and now is the time for Jigsaw's final revenge. The ending of Saw 3D echoes the ending of the first Saw: Gordon locks Hoffman (chained to a pipe) in the very same bathroom Jigsaw locked Adam in, but since Hoffman crossed the line by killing Jill, Gordon doesn't provide him with any means to get free, not even a saw, leaving Hoffman to die.
Game over.