I really enjoy extra material, though I get it mainly through youtube. But it opens up so much, and it enriches a lot of internal debates over episodes or films.
Like the dune buggy discussion from earlier: when I saw the behind-the-scenes interview with Patrick Stewart on Nemesis and he's making it clear the buggies were his idea, that's something I absolutely had to see for myself to believe. I wouldn't have believed that had I read it somewhere or had anyone else told me, "Yeah, the buggies were PS's idea, not Berman's or the studio's." It's not that it made a difference in a big way in terms of my overall opinion of the movie. It's that there was value in seeing and hearing those words come out of his Shakespearean, buggy lovin' gob just settled that internal struggle about WTF is this buggy doing in my ST film?
The behind-the-scenes stuff on Trials and Tribbleations is another one that really enriches the episodes. It's such a fan favorite, and it's pandering in all the best ways, but when you watch those vids on the writing and production behind it, it makes you realize that it wasn't just "coasting" on technology, it was probably a career highlight for all of the production people involved. It doesn't make the episode more or less fun, it just adds that little bit that finalizes your opinion on the episode.
I'm talking a lot of BTS material, but deleted scenes, alternate takes, I love all that stuff. I think my favorite extras are usually interviews with writers, who seem more capable in discussing characters in a Big Picture way. Actors/producers tend to reduce things to scenes, whereas the writers are always eager to provide context.
Anyhow, if they include that on the TNG Blu Ray discs, I'm all over it. And not just on youtube, I might even consider picking up a couple of the stronger seasons if I found them on sale somewhere.