I like watching TV series from start to finish. My wife is rather simple in her tastes, so, we recently watched Cheers from start to finish. Took a few episodes to get going, but, not bad for a sitcom. We may move to Frazier next. We did that with How I met Your Mother, but that is still going. We watched all the episodes until the current season straight through, and then are watching this season week by week.
We also watched Twilight Zone, how's that for a classic? But, of course each story is completely independent, so, it doesn't matter the order. And we had to buy the Season 4 DVD's as Netflix doesn't have season 4 streaming, the season where the episodes are 1 hour. So we watched seasons 1, 2, 3, and 5 streaming, then bought season 4 on DVD.Blu-ray actually. Kinda funny buying a 60 year old B&W TV show on blu-ray.
We watched all the Alfred Hitchcock Presents that are on Netflix streaming, but there are more seasons to come. Those are overall really good.
Now, I loved, loved, loved Buffy the Vampire Slayer and Angel. If you haven't seen those, highly recommended. Don't let the silly premise or title fool you, fantastic shows.
As others have mentioned, Babylon 5. That show was from the beginning intended to tell a "story arc" as John Michael Stazinski (sp?) said it. The acting wasn't always too great. But the writing was excellent.
Reactions to Lost certainly vary. Many people loved it all the way through, but hated the finale. Some only liked the first few seasons, but thought it fell apart after a while. But I liked it all the way through. As far as the finale, I was expecting it to have to be something like it was. So I wasn't disappointed. But one thing I can say, it seems like most people at least liked the first few seasons. Not everybody of course, there isn't anything everybody likes. But I would recommend it. If you don't like it, you aren't compelled to keep watching.
Star Trek Deep Space 9 was really good its last few seasons. I didn't care so much for it in the beginning.