<<< For all of you (none of you) wondering where my avatar is from, it is Johan Liebert from the show Monster.
So it's not on netflix but it is on watchcartoonsonline.com but Monster is a great show.
It's about this neurosurgeon, Kenzo Tenma, living in Germany who saves the lives of these two twins whose parents were murdered in their home. One of the twins turns out to be *spoilers but you find this out in like episode three* an enormous psychopath (cough antichrist cough) and his career is essentially ruined because of it. He then spends the rest of the show trying to track down and stop Johan from murdering everyone ever. Brilliant show. 74 episodes so it's kind of long.
I also recommend:
Cowboy Bebop (Best anime, no it's not debatable) - 24 episodes , all of them glorious
Trigun (26 episodes, I want to say?)
Neon Genesis Evangelion (Watch the original show or watch the three remake movies that just retold the whole show, IMO, the movies don't quite capture the same atmosphere the show did for me but to each their own. 20 something episodes too.)
Those three anime are about as "bread and butter" as universally critically acclaimed anime get and I think everyone can enjoy them, not just anime fans.
20 minutes an episode, basically, so they are super bingeable.