The first "blast from the past" game is Which Witch?. I had totally forgotten about this game until I saw this photo:
This was a fun little game wherein hapless visitors to a haunted house try to go through all four hazardous rooms and climb the stairs to the attic. The game was largely lame, except for the single fun mechanic where you were prompted to occasionally drop the little metal ball down the chimney. The chute split into four directions, which would send the ball down into one of the four rooms, in all likelihood triggering a trap. If your pawn was standing in the wrong place, the trap would hit it, and bad stuff happens to you. The only real reason to play the game was dropping the ball to see what happens. Would it come barreling down the stairs to the attic, knocking down the player who is about to win? Would it hit the broom, or trigger the secret door? Who knows?
Of course, it's just a random event like anything else in these simple kiddie board games, but the kinetic, visceral nature of this random event was immensely more satisfying than the notion of rolling a die. I recall spending quite a bit of time experimenting with the chimney to see if dropping the ball a particular way influence where it came out. Turns out there wasn't, but dropping the ball was fun enough that it kept me occupied for a good while.