Some of these are shows that have already finished as opposed to on-going ones, so they're more "binge watch in a single lost weekend" then "tune in every week".
1) The Tudors/The Borgias (Showtime production)/Borgia (Sky Italia/Canal+ production)
All three sit firmly in the Pillars of the Earth/a sort of historical version of Game of Thrones niche. The Tudors deals with Henry the 8th and the two Borgia shows deal (fairly obviously) with the rise (and to some extent fall) of the Borgia family in Papal Italy. Expect plots, murders, assassinations, machinations, a few pretty impressive set pieces and a lot of bodice ripping.
Arguably the most influential TV series of the modern day... and one that never really gets the credit it deserves for that... this was the first of the adult HBO dramas and as such paved the way for pretty much everything that's come since; Sopranos, Walking Dead, Game of Thrones, Boardwalk Empire, the Wire etc etc. A prison drama with a diverse cast of interesting characters there's a large number of deaths, some interesting cod philosophy, ongoing stories and significant amounts of prison rape. One word of warning; the producers thought they were being cancelled at the end of Season 4 and so wrapped up pretty much all of their storylines... only to find they'd been renewed. As such the two last seasons are, despite some interesting elements, a clear step down from the first four.
3) House of Cards (both the BBC and Netflix versions).
If the political schemes and "magnificent bastard" tendencies in Sons of Anarchy and Game of Thrones get you going then this could well be the one for you. The original is set in the British parliament, the remake in the US political system and deal with how a politician who has been rejected for high office proceeds to ruthlessly exploit everyone in his way to get to the top of the greasy pole. Personally I slightly prefer the BBC take but it looks fairly dated and for someone in the US the Netflix take may touch on more familiar aspects of political life.
4) Person of Interest/The Blacklist
Conspiracy thriller/"... of the week" episodic TV. Both follow roughly the same theme in that they have a "take down the baddy of the week" plot week-in, week-out but tie that into a wider conspiracy theory. Person of Interest deals with a rogue special forces vet/secret agent who works with a reclusive genius billionaire to save lives using a machine that can predict when a person is likely to be murdered and ties into a wider conspiracy within the US government. The Blacklist deals with a genius criminal from the FBI's most wanted who gives himself up to FBI custody and assists their agents in taking down the most dangerous criminals they're not aware of.
Sometimes sold as a French version of the Wire it follows the Law and Order format of concentrating on both the police and judicial system and the Killing format in that a single murder at the start of the series is the driving force behind everything else to come. Well written, well shot and well acted although the need for subtitles may be off putting to you.
6) Spartacus (Blood and Sand, Gods of the Arena, Vengeance and War of the Damned)
If you were watching Pillars of the Earth or Game of Thrones and thinking "what I need is less plot and political scheming but even more breasts, glistening torsos and over stylized ultra-violence" all combined with some dialogue that switches between the overly epic and hilarious seemingly without warning then this is the show for you. It's shot like it's 300 in TV form, there's almost as many pairs of breasts as there are splashes of blood, the language is a wonderful combination of profanity and almost Shakespearean delivery and it's just good fun.