Is willing stuff directly to one's grandchildren a common expectation these days?

I don't know if it's common, but it's not unheard of. My maternal grandmother left a lot to my brother and me, rather than my mother, as we were minors and so didn't have to pay tax on it. If she'd lived until we were adults, she might have changed the will, who knows? Paternal grandmother did live into our adulthood and left us a small bequest each, the majority of her estate going to my father and his sisters.