That little piece of music at the start just sets the tone so well. And the narrative is awesome
[Abe's Oddysee intro video]
This. Although I usually only watch intros once, I saw the demo intro numerous times. The "This is Rupture Farms" quote is something that pops into my head quite often however many years down the line. I was surprised to notice that the final intro is different. In the demo intro
Abe says "Get me outta here! And help me rescue the others" (which I now realise I've been misquoting as "and rescue the others" but whatever. But that's not in the final intro at all.
Abe's Exoddus's demo intro is also one that has the stuck with me. The music, the image of the moon, and the blind mudokuns (which freaked me out when I was younger).
The Soul Blade demo sequence also made me want to buy the game (though I never did because I never used to buy my own games back then).
To contribute an actual game intro to the topic, I think I'll go with this:
Micro Maniacs. I love the music, and the weird scene of assembling V4. Ah... memories.