At least five cinematic videos were scripted, but not included in any known version of the game. The original "Act 1" video described below is known to have been created. It is currently unknown if the others were rendered, or only existed in script form.
The descriptions below were obtained from the cinematic dialogue script available in the Blood Omen Scripts article.
Act 1 (Original)
This cinematic would have depicted Kain's murder, rather than it being presented in-game. It is discussed in Murdering Kain FMV. Later documentation refers to the introductory cinematic as "Act 1", while earlier documentation uses that label for this deleted cinematic, and called the introduction "Intro/Cycling Demo/Act -1"
This cinematic would have involved Kain drinking blood for the first time immediately after killing his assassins, rather than learning to do so in his mausoleum.
This cinematic would have occurred sometime after meeting Ariel at the Pillars, but before Kain's battle with Malek. Its intended content is currently unknown, as it was deleted sometime prior to 22 August, 1995 (the date of the cinematic dialogue script, which is the earliest known reference material).
This cinematic would have depicted Kain escaping from Malek's bastion via "a long, tortuous dust slide", followed by the bastion exploding.
This cinematic was intended to direct the player toward Willendorf. In it, Ariel tells Kain that "the Legions of the Nemesis are on the march from the north", and that "Weirstein and the Stahlberg have already fallen". A modified version of this dialogue was eventually used in-game, rather than for a cinematic.