I have a shell script which contains the following:

case $1 in
    0 )
    echo $1 = 0;
    OUTPUT=3;;
    1 )
    echo $1 = 1;
    OUTPUT=4;;
    2 )
    echo $1 = 2;
    OUTPUT=4;;
esac

HID=$2;
BUNCH=16;
LR=.008;

Are semicolons completely superfluous in the snippet above? And is there any reason for some people using double semicolons?

It appears semicolons are only a separator, something you would use instead of a new line.