The Saw movies have a really bad rep, and I felt the need to point out (for all who will believe me) that it only deserves half of that rep. Is it every bit as bloody, horrifying, awful to watch, and nasty as you think? No. Actually, it's worse on all counts. No, really.
Is it mindless torture porn? Absolutely not.
Saw has a story -- and a very decent one, if you enjoy psychological horror -- and usually has valid reasons for turning the gore dial to 11. Occasionally it doesn't have those valid reasons (hence the 4/5 stars), but most of the violence isn't gratuitous, and those who think it is show their ignorance of the extremely complicated and layered plot (I can completely understand if you couldn't stand to watch it long enough to get the plot, but don't judge on what you haven't seen, please). I really enjoy the serial storyline -- you have to have been on board since the first movie to understand what's going on, and every movie keeps the audience on their toes and requires sustained and careful attention to appreciate the various stomach-dropping endings.
Saw wrestles with some really interesting psychology and has some great characters. I don't think it's appropriate for children with the exception of the particularly-mature mid-to-late teen, but there's a lot to like here if things like Dexter or Law and Order are up your alley. At the "invincible age" where teenagers often make reckless decisions, there are good things to learn here if put into the proper context. I agree with Tobin Bell ("Jigsaw") that anything that makes young people ask questions like, "how would I live differently if today were my last chance?" is a good thing.
Don't say there's no story just because you can't keep your eyes open long enough to get the story. These films are not torture porn.