I was going to mention they are a feature in Shmups but I see I've been beaten to the punch. I think it's a Feature in DOA2 Hardcore, when you beat somebody by tossing them into a stage hazard the game slows way down. I don't remember that happening in other versions.
The main one I always think of is Gradius III. Get 4 rotating options and the laser power up. Pretty much if any enemies are on screen it'll slow down a good bit. However this actually is an advantage because without the slowdown the game would be even more difficult. Mega Man X has some slowdowns in some spots, but it doesn't cause serious issues either. Mega Man The Wily Wars on Sega Genesis "features" crazy slowdown. Even in the battle with Cut Man, only you and Cut Man and maybe his cutter are in play and the game slows down a lot. This didn't happen on the far less powerful NES. Apparently the game was programmed poorly. That is the case with many games with slowdowns. They are programmed poorly. However sometimes it is just because the CPU is overwhelmed. One Famicom game I seem to recall getting slowdown in was Holy Diver. What made the slowdown really bad was that the music slowed down too! For some reason they programmed it in a way that when the framerate can't be maintained it also doesn't maintain the tempo. It makes the slowdown far more noticeable. I once remember some people claiming slowdown was "on purpose" because if you didn't the game/system would crash. It was a silly idea but they believed it.
] I haven't played DOA3 in ages, nor regular Non Hardcore DOA2. I miss DOA3 i think that's my favorite game in the series.
It's funny Alien Soldier lets you actually slow the game down when you pause to make getting through the levels easier.
I was always kinda curious as to whether the big explosions of a boss in Ikaruga and various other dreamcast shmups (which cause the system to literally crawl) were intentional or not. I could see it as a feature as you just defeated a big boss and now you get to watch the aftermath and destruction you wrought in greater (slower) detail. Slowdown was definitely not a feature in many Atari Jaguar games. Checkered Flag comes to mind of a game that is virtually unplayable due to slowdown and framerate issues (and control issues).
Whenever a game would slow down from someone's super/special attack in an RPG I use to think it was just for dramatic effect.
It actually is for cinematic effect up to a certain extent, though. The slowdowns during the boss explosions are still existent on the Gamecube and 360 (although the framerate doesn't drop as much as on DC) for this reason. On another note, the slowdowns in Ikaruga are also important to the gameplay and difficulty balance. The original Naomi/DC-version had slowdowns at exactly the right places when precise movement was required, for example in section 3-2 (up-down ships) or in hard mode's final boss of chapter 5. Beating the chapter 5 boss on hard mode is significantly harder and almost impossible without dying if you play the Gamecube-version, which lacks all of the otherwise massive slowdowns in that particularly difficult battle. The intention to use slowdowns for gameplay was reinforced when the 360-port was released, as some of the missing slowdowns from the Gamecube-port had been recreated artificially for a better experience.
If you're extra dedicated to slowdown in Ikaruga, make sure to play the PAL GC version, 50 FPS goodness makes sure your game runs slower than the NTSC version at all times!
DOA3 is good, except for the final boss (Omega). He's ridiculously hard, and it seems his only purpose is to make you want to throw your Xbox out the window.
That's actually not true, the PAL-version runs on fake 60 Hz speed. That means it runs in 50Hz, but they dropped a bunch of frames every second in order to make it run just as fast as if it would be in 60Hz. The result is that the game runs fast, but doesn't look as smooth as the US/JP versions. I played Ikaruga on a PAL Dreamcast using a boot disc in 50Hz when I first got it, and that was reeeeeeeally slow. Do not recommend lol.
I do remember sometimes feeling like it was purposely put into slow motion. The worst was drifting into view of an area with more assets. you'd chug for a few seconds. It's not optimized in the slightest. Extremely disappointing as I've just recently tried the PC version.
The most amazing slowdown I've ever seen was Bangai-O on Dreamcast. I don't remember the exact circumstances, but a TON of bullets must have been near me, because when I launched all of my missiles, I watched as a frame crawled across my screen. One of the most amazing things I've ever seen in a videogame.