Given your tastes, you’ve probably already watched:
Lost
Alias
But, if you haven’t watched them, you’ve got to. Both are produced by JJ Abrams, who’s kind of a genius.
I loved Alias and it seems right up your alley. I’m plowing through Lost right now and it’s been amazing. I’m in season three, but my understanding is that there’s a TON of disappointment with the last (sixth) season.
Yay, Bored to Death! (I miss that show. I can hear the theme song playing in my head…)
The American House of Cards has been mentioned more than once, but I’d nominate the BBC version. It’s a trilogy:
House of Cards
To Play the King
The Final Cut
Each is four fifty-minute episodes. Riveting.
The Adventures of Brisco County, Jr. - quirky comedy/western which was unjustly cancelled after its first season. If you’re a Bruce Campbell fan and haven’t watched this, shame on you.
Shameless, based on a UK series (which I haven’t seen)
Touch, despite miscasting Kiefer Sutherland. Similar to Alphas, but actually good!
I"m currently bingeing Nip/Tuck which is going to be pulled from Netflix 7/1. It’s 6 seasons worth though, so better get crackin’ if you want to catch it.
Some more Brit series:
Fortysomething - 6 episodes (stars a pre-House Hugh Laurie, pre-Sherlock Benedict Cumberbatch, and pre-Who Peter Capaldi)
Case Histories - 2 seasons, so far
New Tricks - multiple seasons
Blackout - 3 episodes (stars Christopher Eccelston, Andrew Scott)
Inspector Lynley / Inspector Lewis - multiple seasons
Doc Martin - multiple seasons (stars Martin Clunes)
The Town - 3 episodes (stars Martin Clunes, Andrew Scott)
Boardwalk Empire
Sons of Anarchy
The Fall (a British crime drama available on Netflix)
**Broadchurch **(another UK murder mystery, starring David Tennant. Not sure where to find it online.)
Downton Abbey
Elementary
If you appreciate adult entertainment, I would recommend Doc Martin. It’s a British comedy/drama series and there are several threads about it here.
Also, if you’ve never seen Holly Hunter’s vehicle “Saving Grace”, it can be fairly enjoyable - but only if you like Holly Hunter - and I really do.
One show I would caution you to avoid is “Major Crimes”. A lot of people here really like it. If you ever watched Kyra Sedgewick’s vehicle “The Closer”, Kyra left the show after many (far too many) seasons and Mary McCormick (spelling?) took over.
I enjoyed The Closer for a season or two but then it just got horribly repetitive and stupid (just my opinon and I know most people will disagree). But Major Crimes is just a continuation of that show except that everything is only about half as good as it was before the change in command. And I found it really piss poor before the change. So you can imagine how I feel about it now.
Anyway, you should try it for yourself to get to your own opinion. I am cautioning you against it because I find it really insipid, stupid, boring and a waste of a lot of good talent. But see for yourself.
Netflix has the entire Clone Wars series … I dunno about binge watching, but it’s a nice little sci fi hit when you need one. The graphics are very nice indeed, as you might expect from Lucasfilms, and the stories move right along. I also found that it was nice the way they humanized some of the clones. Fighting against droids that could not feel and with Jedi that had superhuman powers they were the Red Shirts of the series, but they often showed great courage and initiative.
Arrow is a lot of fun–the best TV treatment of a costumed superhero that I’ve seen. Season 3 recently ended.
Rectify is a pretty slow-paced drama about a man just freed from death row, but it’s very good and there are only 6 episodes in season 1. Season 2 starts Thursday night.
Longmire is great–about a Wyoming county sheriff and his deputies. More exciting than it sounds.
I believe all of these are available on Netflix.
No, House is largely episodic. “Serialized” refers to a long story broken up over multiple episodes. House had some serial story lines, such as his drug issues, but as you noted the show was known for repeating a certain formula over and over.
Dollhouse is pretty good, it’s got the same brilliant dialogue as firefly.
If you haven’t seen Firefly, then why are you wasting time on the SDMB… or eating… or sleeping. Watch. It. Now. 
http://watchserieshd.eu/category/broadchurch
Another good British police series is Heartbeat, set in a small town in the 1960s:
http://www.tvmuse.com/tv-shows/Heartbeat_25820/
Don’t think Scott and Bailey and A Touch of Frost have been mentioned yet:
http://www.free-tv-video-online.me/internet/scott_and_bailey/index.html
http://www.free-tv-video-online.me/internet/a_touch_of_frost/
Ooh, thought of another good one: True Detective. If you have HBO On Demand you should be able to watch the whole first season. 8 episodes, and it’s supposed to be an anthology series so it’s a complete story, like an 8 hour movie.
The “whodunit” part of the story is good but not as interesting as the interplay of the two main characters played by Matthew mcconaughey as a damaged nihilistic detective having an existential crisis and his partner, a more conventional thinking but morally complex character played by Woody Harrelson. McConaughey’s character Rust cohle has some fantastic, priceless lines about the pointlessness of human existence that if you read them (and I have a website of Rust Cohle quotes bookmarked) they don’t sound anything like real dialogue, but mcConaughey manages to pull it off.
Nitpick: season 2.
DCI Banks from the UK. 20 episodes so far and counting. Two episodes per “crime” so a bit longer format that most procedurals. Airs on some PBS stations in the US with two-episodes-in-one.
orphan black is very good. and on the upside, binge now and you only have to wait until the end of the week for season 2 finale!
are you watching firefly now??!! why not??!!
Daughter and I are currently working our way through Parks & Recreation. On the surface, it bears little resemblance to the sort of qualities the OP mentioned he’s looking for, but fundamentally, I do not care. It is a delightful show, and I endorse it without reservation.
Hannibal
Season 2 is airing at the moment. I only found the show about two weeks before season 2 started, watched one episode, then binged on the whole of season 1 in three days. It’s one of the very few shows I recommend to friends, well worth a watch.
We watched one episode last night. I really wanted to like it, but it failed on pretty much every level for me.
If you enjoy espionage thrillers, few can surpass Reilly, Ace of Spies with Sam Neill playing the part of the historical British master spy. It’s a twelve part mini-series that originally aired in 1983 on BBC. Superb. It can now be found on youtube, but is available on Netflix only on DVD.