Is there a way to keep the screen steady in Smash Brothers?

For Melee, the 20XX Melee training hack pack offers the option to disable screen shake.

I don't know about the other games in the franchise.

To be honest, I've never heard a complaint about the screen shaking before - most people I know (mostly non-gamer relatives) don't even notice it until it's pointed out. You might just be one of the unlucky ones who can't handle pseudo-unpredictable shaking as well as other people can.

There is no in-game option to change screen shaking in any game. There may or may not be hacks to do so, but I'm not aware of them.