I concur with Red and Shawshank Redemption - great movie and fun to see the old glove in there. Another movie I enjoy (and I'm probably the only one on earth) is Walk Hard: The Dewey Cox story - there is a scene at the end where is he trying to reconcile with his numerous children/grandchildren and is playing catch with all of them. Although they got the wrong era gloves for the scene it still cracks me up.
As for TV scenes, I particularly enjoyed the Lost episode where Richard gives Locke some items to choose from (hoping he'll pick the compass) and one of them was the baseball glove. Richard and I were both deflated when he picked the knife (but for different reasons).

Also, classic Simpsons exchange:
Homer: You know, when I was a boy I really wanted a catcher's mitt, but my dad wouldn't get it for me. So I held my breath until I passed out and banged my head on the coffee table. The doctor thought I might have brain damage.
Bart: Dad, what's the point of this story?
Homer: I like stories.