I first got the notion of multi-phase boss fights from kids cartoons. In Battle of the Planets, when a fight got really bad the various team members would combine their powers and turn their ship into the awesome fiery phoenix … which would then kick serious arse.
Admittedly I didn’t think “Hm, a 2 phase boss fight. Note to self: make sure lazydin puts up fire resist aura in phase 2,” but that was because I didn’t have the wealth of raid leading experience then that I do now. Also they were the heroes so you weren’t really supposed to spend too much time thinking about how you’d fight them. (Am I the only person who spent serious amounts of time as a kid thinking of ways to confound Doctor Who in case I grew up to be a space baddie?)
This weekend we had some good attempts at the 10 man Trial of the Grand Crusader (ie. heroic edition), and it brought home to me how much I prefer leading progression raids through multi-phase encounters to single phase ones. The reason is because it is much easier for everyone in the raid to get some feedback on how we are progressing. If you start the night with wipes at about 5s into phase 1 and end the night getting solidly into phase 3 on every attempt than everyone can feel as though it was a good solid night of learning. Even though you might not have actually killed the boss.
I think this is key to the idea of making learning fun in groups. After each failure, you get to tweak something about the raid or the tactics and try again, and get some instant feedback about whether that helped or not. The phases help by ringfencing different parts of the fight. It’s a more interesting way to judge how the learning is going than saying ‘We got him to 42% that time, that’s a 2% improvement in efficiency over the previous attempt.’
Also the WoW raid fights tend to have fairly spectacular phase change animations which at least keep everyone awake. Or give them a chance to adlib amusing commentary to the inevitable long speeches and keep everyone else awake.
On the other hand, I’m not so fond of the phases on farm raids where I have to actually explain them to the person who hasn’t been there before and didn’t read up on the tactics. The worst WoW culprit I can remember was the 5-phase horror of Zul’jin. Firstly it wasn’t that fun of a fight anyway but you also couldn’t really expect a newbie to remember 5 phases worth of instructions (cluster on this phase, spread out on this phase, run away from whirlwinds in this phase, etc etc) off the bat.
Our raid leader wrote a macro for that one in the end.
Welcome to Spinksville! 
My personal Nemesis was Kael’thas in Tempest Keep.
You just had to mention Zul’jin. I am still peeved we couldn’t down him before 3.0 dropped. Eagle phase is the stuff of nightmares, we had such unbelievable issues with it.
I enjoy phases as well, in a fight like Mimiron or Thorim it’s very easy to tell if you’re making progress or not. I hate Freya though. For us she breaks us in P1 every time, always the wave of 3 Elementals, and once those are down, it’s a walk in the park. Frustrating. I dream of one-shotting her, but it’s just not happening.
Zul’Jin as a prot warrior was actually some of the most fun I had in TBC. Just learning the encounter was more fun than anything in that entire instance (and it WAS a good instance!), kinda like Mimiron in Ulduar these days.
I love phases. Mostly because it gives me a chance to pop a nightmare pot its true……
Seriously its good to have markers and goalposts to all these fights. It gets annoying when like with a certain Blue Dragon they throw a huge gimmick into the mix on a long multi phase fight. In a way Icehowl is a bit like that. If the dodge-the-charge-or-wipe moment came at the start at least you could learn it and them move onto the hard stuff…rather than have to rince/repeat the entire fight just to learn that. Mind you much less annoying than Maly/dragon riding.
Gimmicks apart I like 🙂 (and we’re so getting icehowl next go around)