Not voting due to no "Other". It totally depends on the music.
1: Unstructured
If you are going to scream, don't make it sound too chaotic - make it sound like it was MEANT to be there, not tossed in as an afterthought.
For instance, we have "Surrounded by Silence" by Design the Skyline - all the screaming just plain old doesn't work, due to being set up wrong. The first part of the song is borderline pretty... and then... well. Just listen.
<spoiler=Surrounded by Silence - Design the Skyline><youtube=ViSZI6UJEUQ>
Also note that the chorus has different structure entirely from the verse, which would be OK (if not kind of amateur)... and then the screaming comes back and changes the structure again. Not cool, guys! And then the ending. Oh the ending. This is how you don't do "intense screaming song". ("buuuurrrrrp bur burp burp burp buuuuuurrrrrrrrrrrrp")
This kind of music has its fans, and freeform screaming has its appeal, but I'd much prefer...
2: Semi-structured
Now, some would say that Design the Skyline just can't scream. That may be the case (I'm no expert), so let's look at a song I actually kind of like...
<youtube=KDzt6yI3Dw8>
While this song is rife with thematic, stage-show and structural issues (skip to 2:40 for my personal favorite musical WTF ever), but at least they knew what they were doing with their screams! While they can't seem to knit two musical ideas together, the screaming actually meshes with the nearest surrounding music (mostly, via black magic), so it's certainly more listenable than Design the Skyline. I'll call it a guilty pleasure.
3: Proper
I'm positive that everyone here reading this has their own collection of screaming music that they adore, so I don't think I need to cover it, I can't possibly cover everyone's taste in the general "hardcore metal" screaming area, and I don't want to analyze it all. Tons of great artists do it, like Pantera, or Nine Inch Nails. It's just that I don't really care for that kind of music. Specifically, it has verse-chorus structure with some/many/all of the words screamed instead of sung. All it has to do is follow ONE musical idea (or several if they can do it right) without terrifying breaks in tone to be structured. It can be good music, I just don't really care for it, as it's not as interesting as semi-structured (PERSONAL OPINION ALERT), and not as effective and hair-raising as...
4: Primal
Typically, For something to be primal, it has to be ALL ABOUT THE SCREAM in the moment. THAT'S the kind of screaming I can truly appreciate. Interestingly, it doesn't come from metal very often (as far as I can tell). I've had most luck finding primal screaming in industrial music... and electronica.
<youtube=QT8zdnaxyME>
(Note: The song is not actually from the Embryodead album, from what I can tell. Unless it's the bonus track.)
Hear the chorus? Particularly the last one? It's not screaming words of anger and rebellion... it's just SCREAMING.
Just... AAAAAAAAAAAAUUUUUUUUUUUUUUUUUUUUUGGGGH! The ending is by far my favorite screaming moment in music, it's one of the two screams that consistently makes me shiver.
The other is held by Aphex Twin, of all people.
<spoiler=Come to Daddy - Aphex Twin><youtube=tWDAtMPoBHA>
4:10 is relevant. Same thing - it's all about the WAAAAAAAAUUUUUUUUUUUUUUUUGH. It also appeals to me that on the official lyric sheet, the entire thirty seconds of primal aggression is denoted by "Argh".
So, to sum up, I like barely structured screamers if only for the novelty, but if you want to truly IMPRESS me with your screaming, you have to make it as primal as possible.