Most of the US series do get screened here (though often on the subscription satellite & cable services). I must say that I tend to record a lot more than I watch - so am often well behind, and sometimes have to write off a series when I've hopelessly lost track of the story lines.
Currently, I'm plowing through Game of Thrones - an intricate complex of story arcs. I think I'm somewhere on Series 4. I'm practically current with Blindspot, so will watch the new series. Blacklist is one of those that I lost track of (regretably), so I'm not recording the current series (at some point I'll try to download the episodes I missed from Box Sets (which my subscription covers).
I do try to watch the fantasy series based on classic comics (Supergirl, Flash, Arrow, Legends, and the one with Skye/Daisy in, whose title slips my mind). I've lost track of Arrow (cue for Kacey Musgraves to help with a song, lol?) - so that's another one for the Box Sets some day. (Talking of songs - kudos to the Supergirl producers, for playing a snatch from a Margo Price song, in the alien/gay bar scene recently)
Nashville was a favourite of mine, because of the theme, Callie Khourie's vision of the industry, and the musical direction of, firstly, T-Bone Burnett, and then Buddy Miller - which I found often significantly better than the radio take on Nashville's output, and included some strong songwriting. We are late in screening this (and it has hopped channels), but I haven't found our latest series (the third?) to be quite as good. I'm not even sure that we'll get the next one (which was saved from cancellation by a CMT deal - unless someone else buys the rights (CMT doesn't have a channel here.) In any case, not having Layla Grant (Aubrey Peeples) would leave a big gap for me.
Two series which sound promising, and I've recorded, but haven't yet watched are "Westworld" and "Into the Badlands".