I don't even see how it's possible that this thread is on page three and nobody has mentioned Buffy yet. In my opinion, it's the best show in the history of television. Another show that I love which also hasn't been mentioned yet is Veronica Mars. These are two shows that absolutely everyone should see, period. They are shining examples of TV at its finest.
I agree with others who recommended The Wire and The Shield. These are both phenomenal shows that make for great binge watching.
I'm surprised there haven't been more comedies mentioned. Malcolm in the Middle is one of my all-time favorites. If you only know Bryan Cranston from Breaking Bad, you will be amazed by how versatile of an actor he is. Some of my other favorite comedies include:
Curb Your Enthusiasm
The Larry Sanders Show
The IT Crowd
Parks and Recreation
Eastbound & Down
It's Always Sunny in Philadelphia
Party Down (created by the same guy as Veronica Mars)
Better Off Ted
As far as more modern dramas, I have to echo all the recommendations for Westworld. I found it to be one of the most compelling and well done shows in a long time. Some other recent shows I really enjoy include:
Lastly, if you haven't seen it, you absolutely have to watch a show from 2006 called Day Break starring Taye Diggs. Most people have never even heard of it, but its so amazingly good and perfect for binge watching. It only lasted one season, but it has a complete story arc with a satisfying conclusion. There has never been a single person I recommended this show to that didn't love it.