Speaking
as a grandpa, one who helps grandma babysit our 3 year old granddaughter...
Just before Christmas I ordered her, then read to her, some classic fairy tale books: Little Red Riding Hood, Rapunzel, Jack and the Beanstalk, the Three Little Pigs...
I sit and watch the Backyardigans with her. (Or at least, I did until
this.

) But to broaden her cartoon knowledge and appreciation (not to mention her sense of the absurd), I ordered and play for her some of the classic Looney Tunes cartoons. You can't really say you've had a childhood unless you watch a coyote repeatedly fall off a cliff.
We rassle on the floor, I tease her, she teases back. (Just yesterday she and grandma conspired to stick a couple of potatoes in my shoes. So when I went to put them on....)
And just to encourage her sense of absurdity, I make up bizarre stuff. She usually arrives in the morning a few minutes before I finish my morning shower. So when I'm dressed, she's in the living room at the foot of the stairs with grandma. Before I come downstairs, I'll do something ridiculous like make a bunch of barnyard noises, then come downstairs complaining about how difficult it is to get around all the chickens and cows in our bedroom. That kind of stuff always brings a grin to her face. (Although I still haven't figured out whether that grin means "Grandpa's entertaining," or "Grandpa's nuts.")