If you look back at the N64 version, the screen hardly ever shakes/rumbles/tremors. I believe it only shakes during bombs and some select heavy attacks.
In the Melee and Brawl versions, however, it is almost non-stop. I have always found it annoying and that it made it hard to play long sessions and hard in general to track players. This is especially true when two people are beating each other up on the other side of the screen, the camera is zoomed out, and I am trying to fight someone else. When I do a 1v1 the screen shaking basically doesn't bother me.
Is there an option or a cheat to turn off screen shaking?