The decision-making process went something like this:

"There is some unfinished business in my Lament screen saver. I really ought to add the last few moves to that."
"...Hmm, I guess I need to watch the movie again to make sure I got it right."
"...Hmm, I wonder if any of the later movies added new cube behaviors?"

1. Hellraiser

   Wow, is this movie dated! It's so 80s, with its giant shoulder pads and nuclear family and unfamiliarity with guys in gimp suits with lots of piercings. I remember this being a lot gorier and more shocking than it seems now. Some of the practical effects hold up reasonably well, but it's really not that great a movie.

   The cube goes through the four basic moves, plus there's an impossible shape during the scuffle at the end. It looks like they broke two of the models and just glued them together randomly.

2. Hellbound

   At the time, I remember thinking this wasn't as good as the first one, but now I think it's a lot better. The Channard and Tiffany characters are pretty interesting, and the whole Leviathan situation is pretty cool. There's really a lot more running and screaming than there needed to be.

   Two new cube behaviors: the opening door, and the transformation into Leviathan. The Leviathan transformation annoys me because some of the pieces of the cube just fade away in a jump cut, and it doesn't even remotely conserve mass. But they are in a hell dimension at the time, so... ok. Also, they changed the orientation of the faces. I assume that was an accident.

3. Hell On Earth

   This movie is absolutely terrible. They even made the "evil owner of an evil nightclub" boring. (The Crow did that trope much better.) They turned the Cenobites into low-rent late-period Freddy Krugers. This one dimensional character is a cameraman, let's stick a camera in his head. This guy's a DJ, he can shoot CDs out of his mouth. Oh, and since we have a female lead, don't skimp on the daddy issues! Ugh. This is definitely the second worst of the entire series.

   One new cube behavior: a tower pops up and zap, zap, zaps Cenobites. Also, instead of having six distinct faces, the cube only has three faces that are duplicated. Come on, guys, can nobody keep track of the original props?

4. Bloodline

   Overall, this movie is awful, but it has some good scenes. I really enjoyed the fifteen minutes or so about Lemarchand creating the box, and the Angelique character is kind of interesting, as a Cenobite who predates the gimp-suit fashion trend taking over the hell dimensions. The rest of it is crap: the 90s plot is crap, the Hellraiser In Space plot is crap. I liked the idea of the office building that was itself a Lament Configuration, though they didn't do much with that. Directed by Alan Smithee: probably his finest work since Dune.

   One new cube behavior: instead of the door opening as a square, it opens as a pointy octagon. Nothing special.

5. Inferno

   This movie is not bad. But it's only barely a Hellraiser movie. It's a noir-ish story about a dirty detective chasing a serial killer who (dum dum dum) might be himself. The extremely small amount of Hellraiser fu in it leads me to believe that the first draft of this script wasn't a Hellraiser movie at all, before they re-tooled it.

   No new box behaviors, since the box barely appears.

6. Hellseeker

   Oh, hey, Kirsty's back! This one is pretty good. Probably the best one so far. Kirsty's jerk husband finds the box, hallucinates wildly, and maybe murders a bunch of his friends. Nice twist at the end.

   One new box behavior, which might have been a dream: it starts out as a sphere, and then turns into a cube. Whatever.

7. Deader

   Deader? They actually called the movie Deader? This is another script that pretty clearly started out its life as not-a-Hellraiser-story, but I think it was pretty good. It's kind of Flatliners Go Romania. How do you run a nightclub in a subway car? Note to self, look in to that.

   One new cube behavior: when the chains come out, the whole top of the box breaks open. Dumb.

8. Hellworld

   This is one of the worst movies I've ever seen. This is some shitty student film that they somehow got Lance Henriksen to be in. This movie is so bad, I think I liked it better when it was called House of Wax and starred Paris Hilton. There are a bunch of assholes who play an online Hellraiser game and someone invites them to a party and kills them all. There's a reason but you will never care even remotely what it is. Or whether any of them live.

   One new cube behavior: nails come out of it. But it wasn't a real Lament Configuration so it doesn't count.

9. Revelations

   Despite the reviews, I must say, I enjoyed this one! Maybe I was a little punch-drunk by the time I made it this far, though. And anything would be a step up from Hellworld. It starts off with some shaky-cam nonsense, but fortunately they didn't keep that up. A couple of jerky bro teens go to Mexico, murder a hooker, and pick up a Lament Configuration from some dude in a bar, you know, like you do. Most of the movie is told as a flashback at a dinner party with their jerky family, when one of them escapes from hell and shows up skinless on the veranda. Antics ensue.

   The box barely moves at all, but the glowing effects are much better. Oh, and the guy who plays Pinhead is the worst. The worst.

So! While I was at it, I also made a supercut of every on-screen appearance of the box, in all nine movies! It's 26 minutes long.

As soon as I posted it, it was immediately blocked with five or six content-ID matches. So I filed a DMCA fair-use counter-claim, and whattayaknow, it was back up less than a day later. I assumed they just ignored those...

Update: Oh, I see that it says the counter-claim is still "being examined". So you'd better download a copy of it in case they change their mind.

Update 2: I am shocked, shocked to report that they have denied my counter-claim without explanation.

Update 3: Success, four and a half months later.