Elliot: Okay, he's a man from outer space, and we're taking him to his spaceship.
Greg: Well, can't he just beam up?
Elliot: This is reality, Greg.
While Elliott and ET are saying goodbye, in the original 1982 version in the shot facing Elliott, ET lifts his right hand to point his finger at Elliott's forehead and ET's finger glows (note the weird angle of ET's raised right hand), but in the next shot facing ET when he says the iconic words, "I'll be right here," it's actually ET's left hand up by Elliott's face. This was digitally corrected in the 2002 version, so that in the first shot ET lifts up his left hand.
Steven Spielberg has a cameo as one of the doctors when Elliot and E.T. are 'hospitalized' inside the house.