Not so much the impact of Star Trek on our own popular culture, but the sorts of pop culture things that Star Trek/Federation characters might be into.
I'm planning a campaign set in the 2290's, right after the Khitomer Accords and I'm trying to come up with some things to help the ship and the Galaxy feel more lived-in and organic.
One thing that struck me about the delivery of culture in Star Trek is the Federation premium on uniqueness. Since manufacturing is fairly easy on civilized worlds (I don't think they're up to replicators quite yet, but advanced manufacturing can do a lot) and Federation citizens have easy access to anything they need, the unique has a special place in the culture. On the most basic level, the experience of seeing a live performance would be more valuable than a recording. The original Enterprise played host to a group of traveling players and music recitals have been the entertainment of starships in the 23rd century.
So how much of Federation culture would be recorded and how much would it be designed to be presented live? Rather than producing a recorded drama show, maybe the company instead releases scripts to be put on by local players, perhaps with codes and patterns for holographic sets and/or automanufactued props.
