Is there a library that will let me load a movie file and play it in an OpenGL application? Or maybe just a code sample that someone has lying around? I'm also using GLUT, if that makes a difference. I guess file format doesn't matter, although currently my movie is in AVI format.
Well, there's this very ancient tutorial that plays an AVI video using fixed function GL and the Windows API.
I don't recommend using this setup, since it is very outdated, but the concept is basically valid. Get each frame of the video and use it to update an OpenGL texture. That simple.
If you run into performance issues, then you can start thinking about optimizing with things like Pixel Buffer Objects.
If you're happy to use the ogg theora format, then you could use the TheoraPlay lib. There's a fully functioning plugin for the Duality engine here that you could use for reference - https://github.com/Andrea/DualityOgvPlayerPlugin. It works with opengl.
First off, you might want to check these questions / answers out. I don't know how much of either is iOS specific, but they might help: