Here are a few on my list:
UK:
Porridge (1974–1977)
I, Claudius (1976)
Playing Shakespeare (1982)
Yes Minister (1980–1984)
The Young Ones (1982-84)
I'm Alan Partridge (1997-)
Spaced (1999-2001)
Little Britain (2003–2006)
Buried (2003)
Mid Morning Matters with Alan Partridge (2010-)
Black Mirror (2011-)
The Hollow Crown (2012–)
Travel Man (2015–)
The Crown (2016-)
Mum (Season 2) (2017)
Peter Kay's Car Share (2015-)
US:
The Honeymooners (1955-1956) (thanks to Dell for the recommendation)
The Twilight Zone (1959-1964) (selected episodes)
Star Trek: The Original Series (1966-69) (selected episodes)
Miami Vice (season 1) (1984) (currently watching)
Behind the Music (1997-)
Dinner For Five (2001–)
The Wire (Season 2) (2003)
Firefly (2002-2003)
What's In My Bag? (2006-)
On Death Row (2012-)
BoJack Horseman (2014-)
Mr. Robot (2015-)
Hip-Hop Evolution (season 1) (2016) (Thanks to Nostra for the recommendation)
Stranger Things (Season 2) (2017)
Other:
Matador (1978-1982) (currently watching)
Historien om Danmark (2017-)
I prefer UK comedy. For drama I like a story (like Twin Peaks or The Wire) that progresses.
Have you seen any of these? Which TV shows are at the top of your queue? What TV-series should I watch next, any suggestions?