My wife and I are currently catching up with Dr. Who on Amazon Prime.
If you’re an anime fan, My Hero Academia is pretty awesome, and I’ve heard The Ancient Magus Bride is also very good (both on Crunchyroll). Fullmetal Alchemist Brotherhood is also superb whether you’re an anime fan or not. It’s hard to explain why it’s so good, it just is. It’s on Netflix. (So is the original, just Fullmetal Alchemist. It’s good, but Brotherhood is a million times better.)
I’ll always recommend Twilight Zone to anyone willing to watch it. It remains probably the best show ever to air on television, and was decades ahead of its time. I watch episodes of it and they relate directly to things we’re dealing with today. (Especially The Obsolete Man…) If you like Twilight Zone-esque stories, Night Gallery on Hulu is also by Rod Serling. It focuses more on Horror, but but it’s still well worth watching. Black Mirror is sort of a modern technological TZ. It’s on Netflix, though I have trouble recommending it. The episodes are frequently unpleasant, and I can only watch one or two at a time, but it’s still generally well done.
Sherlock on Netflix is excellent. It plays fast and loose with some of Doyle’s stories, but as a life-long fan of Holmes, I thoroughly enjoyed the series.
Umm… Burn Notice is pretty good (Netflix), Ash Vs. Evil dead is hilarious if you enjoy that type of humor. (Though, lots of occult stuff in it, so I can’t honestly say I recommend it… if you are a fan of the original movie you’ll probably enjoy it.) It’s also on Netflix. Arrow’s first two seasons are excellent, I haven’t watched much beyond that yet.
If you like crime procedurals, NCIS’s early seasons are superb.
Stranger Things is pure awesomeness… (Netlfix)
Limitless only has one season, it was tragically not renewed despite being the best new show it’s year. It’s got great humor, engaging characters, and each episode is themed in a unique and interesting way… seriously… why did it get cancelled x_X
I hope there’s something in here you like. My wife and I enjoy watching a show with dinner, and i put shows on as background noise at work, so I have a pretty extensive watch list XD.