awk '
    /=/ {
        for( i = 1; i <= NF; i++ )
        {
            if( substr( $(i), 1, 1 ) == "=" )
                $(i) = "__________[" count++ "]";    # corrected
        }
    }
    { print; }

I am =honored to be with you =today at your
commencement =from =one =of =the =finest universities
in the world. I never =graduated from =college. Truth
be told, this is the =closest I've =ever =gotten to a
=college =graduation. Today I want to tell you three
stories =from =my =life. That's it. =No =big =deal.
Just three stories.

I am __________[0] to be with you __________[1] at your
commencement __________[2] __________[3] __________[4] __________[5] __________[6] universities
in the world. I never __________[7] from __________[8] Truth
be told, this is the __________[9] I've __________[10] __________[11] to a
__________[12] __________[13] Today I want to tell you three
stories __________[14] __________[15] __________[16] That's it. __________[17] __________[18] __________[19]
Just three stories.