Assuming you never saw the late 90's classics like Trigun or Cowboy Bebop, here's a few that might be up your alley, just gonna go down the list I (painstakingly) updated a while back om MAL:
91 Days -- Fairly recent one set in prohibition era... United States I think?
Ajin -- Also recent w/ 2 seasons, the animation takes some getting used to but it's a good one. I'd rarely recommend the Japanese audio over a dub but it's worth watching the Japanese version purely for the guy who does the voice of Sato.
Attack on Titan -- You've probably heard of it, hell it's even been airing on American TV. Good action and one of those shows where you probably shouldn't get too attached to any characters.
Black Lagoon -- Another classic action show. Watch the dub, the dialogue and colorful nature work so much better in English.
Death Parade -- Interesting show based off of what I think was a one off OVA or something, plot is a little hard to explain better off watching the first few eps.
Fate/Stay Night franchise -- Personally I never saw the original adaptation from 2006 but from what I hear I didn't miss much. Fate/Zero and Unlimited Blade Works are both worth a watch though if you watch Zero first you'll really hate the characters from UBW. Viewing order doesn't matter though. Fate/Zero is one of the best English voice jobs of any show I've seen and would recommend it.
Full Metal Alchemist: Brotherhood -- I never finished the original FMA airing but from everything I've heard, outside of them blazing through a lot of potential content in the first few episodes of FMA:B, Brotherhood is far superior in every way. Fantastic show and well worth the watch even if it is 64 episodes. Also recommend the dub version.
Ghost in the Shell Stand Alone Complex (I & II) -- The tv series based in the universe. Vastly superior to the movie, highly recommend it.
Jin Roh The Wolf Brigade -- Movie that came out in 1999. Absolutely fantastic, bit of an alternate "what if" Japan in the post WW2 timeframe.
Knights of Sidonia -- Same studio that did Ajin. Think Battlestar Galactica but replace the cylons with some ugly ass tyranid/zerg type enemy. English dub seemed pretty solid from what I saw, I had originally watched it as it aired as the English version is Netflix only and came out after the season(s) had ended.
Mob Psycho 100 and One Punch Man -- Two show adaptations of mangas by the same author. OPM is pretty much a pitch perfect spoof of everything super hero related, especially older shows like DBZ. Mob Psycho is... different? Gotta watch to really get a feel for it. Don't give up after a few episodes, I was about to drop it but glad I kept going.
Mobile Suit Gundam franchise -- I haven't seen them all but if someone wants to chime in with their opinions feel free. The currently running Iron Blooded Orphans is probably the most grounded in reality you get excepting 08th MS Team.
The Seven Deadly Sins (Nanatsu no Tazai) -- Really cool adventure/fantasy show about 7 badasses although the 7th has still yet to be seen in either the show or the manga (I think?). There's a 4 episode OVA series that came out that takes place immediately after the first season and another season should be along at some point.
Overlord -- The only "stuck in a game" series I'll recommend. Considered Log Horizon but there's too much filler and season 2's art just bugs the fuck out of me. Overlord is about a guy who doesn't log out of a video game on the day the servers are supposed to go down and even though they never explain how the tech works I'm assuming it's VR based like a bunch of other "stuck in a game" shows. Servers don't go down and now he's part of the world as, what he thinks to be, the only player still left. NPC's go from just static functions to actually developing personalities and whatnot. Short at only 12 or 13 episodes and I believe a season 2 is coming at some point.
Psycho Pass -- Haven't actually finished it myself but plan to at some point. Similar thematically to Minority Report, future Japan has developed a system that can monitor the mental status of people and whatnot.
Samurai Champloo -- Samurai based show directed by the same guy who did Cowboy Bebop. Watch it in English.
Steins;Gate -- Show based around time travel. Usually I hate that premise but the show is absolutely fantastic. Also one of the shows I'd recommend the English dub on, the cast does a great job.
I'm probably missing tons of good stuff but this is what I could find right off hand
