Yes, I've been to quite a few baby friendly movies in the last 16 months at our wonderful independent theater, which offers two baby friendly shows a week. Over 50 at last count. Enough that my daughter has staked our her own favorite spot to take a break and look out on the street from the theater lobby (second photo).
I've seen some great movies, and have always relished the chance to see a movie while on duty as a parent. It took having a second child to realize that you can actually do something you want to do and take care of you child at the same time. These movies are the highlight of my week.
Here are the movies I particularly enjoyed. I'd recommend all of them, assuming you have movie taste like me, which I'd describe as 'medium-nerd:' Win, Win; Louder Than a Bomb; Bill Cunningham, New York; The Illusionist; The Trip, Another Earth; Farewell.