Family Guy is a TV show known for its humor based on references and cutaways. Here is a list of all the movies that Family Guy makes fun of, as well as episode name/number in the details. I'll put them in order of number of references.

Done Up To: S7E8

Also mentioned, but not on Letterboxd:

Debbie Does Dallas S3E2: Brian Does Hollywood

Deep Throat S4E23: Deep Throats