First, the ratings:
Ninja Gaiden 2: 5/10. The NES is ill-suited to try anything spectacular cinematically, but this intro at least tries.
Soul Edge: 6/10. Decent, but the music then drags it down to make it feel like a Saturday morning cartoon.
Fallout 1: 9/10. 'nuff said.
Homeworld (Remastered): 7/10. While nice overall, it's lacking something to push it into the big leagues. Not even Barber's 'Adagio for Strings' helps.
The Witcher 2: 6/10. This intro demonstrates a problem; improved technologies does not automatically make for better things. While visually and technologically impressive, it does nothing to impress the viewer, or set the tone for what's to come. It's all been done to death before.
Warhammer: Mark of Chaos: 7/10. Now this is more like it.
Flashback: 6/10. Decent cinematics for its time, but the ill-fitted music kills whatever it's trying.
Another World: 9/10. This intro turned heads back when it was released, and it still kicks ass to this day.
Dark Colony: 4/10. A low-res Nope.avi.
Icewind Dale 1: 9.5/10. A good narrator goes a long way towards selling a great intro. Brilliant use of simple cinematography, boosted by excellent audio direction makes this one of the best intros out there.
Eye of the Beholder 2: 8/10. The first intro presented that makes me wonder what it could accomplish with modern technology. But what it does already is quite impressive.
Kid Chameleon: 5/10. It just feels corny to me, but it's short and gets the job done.
Lemmings: 5/10. Same as Kid Chameleon.
Perihelion: 6.5/10. It falls into the same trap as many other Amiga-intros; it plods along and uses too much text.
Syndicate Wars: 5/10. I see what they're trying here, but the early 3D CGI ruins it.
Might & Magic Darkside of Xeen: 7/10. Simple, but effective. The music does it a great disservice.
UFO Enemy Unknown: 8.5/10. A classic.
Syndicate: 6.5/10. Better than the Syndicate Wars-intro.
Republic Commando: 5.5/10. Clever use of a singular perspective at least elevates this from mediocrity.
Diablo: 6.5/10. Honestly? I thought I was watching the intro for Dungeon Keeper. A little too generic, but note how Blizzard's cinematics improve from here.
Icewind Dale Heart of Winter: 6/10. A letdown compared to the original intro. Doesn't impress me, doesn't leave anything.
Empire Earth: 5.5/10. Early-CGI intros have aged badly.
Starcraft Brood War: 7/10. A good cinematic, but not a good intro.
Flinthook: 8/10. Nice one. Gives me hope that the art of the intro isn't dead.
Cyberpunk 2077: 0/10. Rapid-cuts are the bane of intros.
Secondly, my suggestions. This one is widely claimed to be the best intro the Amiga ever produced, I present it without personal comment:
This one gets the dubious reputation of being the longest intro I've ever come across; a 12-minute monster (when you add in the credits) that looks and feels like it spawned from the Amiga... but sadly didn't, as the Amiga-version is a cut-down wall o'text. This is the MS-DOS version: