The offside rule's been there since long before WW1.
They did alter the number of defending players needed to put a player on-side down from 3 to 2 in the mid 1920's.
I'd argue that was altering an existing rule rather than a fundamental rule change though.
Then the other massive change was "no one can be offside when the ball is played" to "no one in an offside position can attempt to play the ball". Totally changed the way the offside trap was practiced, I believe.
The biggest change in my memory was the one that stopped the endless passes back to the keeper by preventing him from picking it up if it had been kicked back. Also worth mentioning is the 3 points for a win I suppose.
