I never cared much about movie rentals as a kid, however growing up in the late 1980s one of my favorite things was renting NES games from local video rental stores on the weekends (they all got into NES rentals pretty quickly).
There was always a bit of a thrill looking for a new game to play through. Each game experience back then seemed remarkably original, like new gaming territory was being traversed for the first time. Going from Ninja Gaiden to Little Nemo to DuckTales to Mega Man and so on.
The only thing better was the massive wall of games at Toys R Us. Originally they displayed the boxes on the wall (they later switched to a lame slip of paper). I vividly remember Zelda's gold box leaping out from everything else.