To take off on Mrs. Mendlebright's discussion "I Just Watched...", I just watched "The Luck of Newton Monroe" and I realized that Ron Howard didn't appear in this episode. Then I got to reckonin... I bet there are at least five or six other episodes in which lil Opie doesn't appear. I can think of a few but I'll let others chime in so's I don't hog all the fun.
According to IMDB, there are 25 episodes without Opie. I took the total number minus the episodes with Opie.
I'll have to check with Johnny Paul Jason.