Sorry, looks like G.I. Joe made it...sweet!
Lite Brite's a definitive possibility. I know it's been around at least three generations, most people from those three generations can identify it by name, and most have played with it. Finally, I think most child development "experts" would find it educational.
I'd say the Rubik's Cube was really only a significant toy for one generation (actually, only a significant toy for about two or three years), and probably wouldn't meet the criteria for induction. I'd consider it more of a fad -- but unlike the Hula Hoop fad (Hula Hoops are in the THOF), Rubik's Cubes won't continue to sell a million or so a year for fifty years, like Hula Hoops.