One of the things that convinced me to play the entire game through was the initial introduction video to Act 1 (hospital scene). The prologue impressed me, it was done better than I was expecting, but that first video really made me sit up and take notice, and realise that this was a highly polished game rather than something relying on gimmicks to get readers to download it.
Since then, I played through Emi's, Shizune's and Lilly's paths (in that order), and obviously watched the intro-videos for them. Emi's video seemed to be a bit of a short story in itself, and was enjoyable but nothing special. Shizune's was good, and showed well the relatinoship between the three main characters, before Misha starting to feel like a third wheel. Lilly's showed how a blind girl see's life, but ultimmately was the weakest IMHO. I've since YouTubed Rin's, and it shows her weirdness well, but aside from that isn't too great IMHO.
However... Hanako's video blew me away completely

Yet again, Katawa Shoujo shocks me with it's professionalism and high quality.