Definitely To Sir, With Love. You really don't even realize what is happening in the scene. Sidney Poitier goes ballistic on his female students because one of them burns a feminine hygiene product in the furnace. It was so taboo at the time that you actually have to look it up to figure out what they're talking about.
Osama - A girl in the Middle East is disguising herself as a boy, and menstruation plays a pivotal part in the film's climax.
Towelhead/Nothing Is Private - There's actually quite a bit going on in this highly disturbing movie, including the poor girl's traditional Lebanese dad bringing her to the store to get pads for the first time and some of classmates stealing them from her.
As someone said, My Girl has a good first period scene, as does Eve's Bayou. Slums of Beverly Hills has one that I would call more awkward than funny. And there's one in The Blue Lagoon.
I remember both Blossom and Roseanne having first period episodes as well. For Blossom, she imagined that Claire Huxtible made her a cake showing her what the ovaries do with icing, while Darlene on Roseanne isn't happy because she doesn't want to be one of those prissy girls like Becky.
Finally, Golden Girls had a great episode when they were talking about "the curse." Blanche tells this story about how she was waiting to get the curse and nothing was happening. Then, the doctor asked her about whether she had her period, and she said, yes, for several years. She just doesn't know what this curse is about.
