From intermediate/B1 (approximately)Edit
One of the most popular series among the learners. Not only is it fun and classics among the tv series. The language presented is mostly everyday American English you can meet in wide range of situations. I would recommend it even as the first series to watch in English.
A sci-fi classics, awesome for learners from the intermediate level +. There is a small number of main characters at the beginning, so you can easily get used to their speaking, and there are more and more new and recurring characters over the ten seasons of SG1 and five of Atlantis. Unless you dislike sci-fi or Stargate in particular, it is a very good show for learners.
Another show I would recommend to people around B1. It is most popular among younger teenage girls (well, perhaps not anymore but ten years ago it was) but can be fun even for a less demanding adult learner. The vocabulary turns around both everyday topics and killing demons (which gets a bit repetitive over time, true). One of the advantages is relatively small number of main characters in the beginnings with others joining later, similarily to Stargate. It is as well a long series so you are sure to get a lot of listening done between the beginning and the end of the story
Once Upon a TimeEdit
Fairytales got into our world because of the evil queen's curse. A complex story using the fairy tale elements offers a variety of characters most of which speak very nice and clear English.
More challenging fun (probably around B2/C1)Edit
A more complex one than Stargate both when it comes to the story and the language by some learners. A good choice for an advanced learner. Classics of the genre.
The Big Bang TheoryEdit
A very popular show about a group of friends most of which work as physicists at university. One of the shows where those dubbing it into other languages should be imprisoned for torture of the viewer and murder of 90% of fun. You can hear a lot of everyday language and a lot about science, sci-fi, comic books and superheroes. However, I wouldn't advice it to intermediates as the speech is quite fast and all the science and comic books related fun might become an obstacle.
One of the many detective series but different. The vocabulary you'll encounter is related to everyday topics, anatomy and anthropology, crime and science. Most actors speak very clear English, especially as most of them represent well educated characters.
A detective/fantasy series inspired by the fairytales. Many characters, most speak nice English. And you get to hear pieces of French, German, Spanish and Latin!
For those considering themselves really good.Edit
One of the more challenging shows. A webseries about a group of players of an online game. Much faster and harder to catch than for example the Stargate or the Friends.
A great series for people learning the English medical terminology and not only them.