Magnitus: I'm a bit conservative with animes.
I don't like it when they act too over the top (though they seem to have at least one character like that in every anime) or if its too gamey (ie, "I reached the next level" or "I just beat that guy and became stronger, the next guy will be even more tough and I'll get stronger to beat him") or when they have a bunch of teenagers playing at being adult (ie, "We are not ready to have sex, but we are totally ready to adopt a kid").
With that said, I mostly enjoyed:
- Psycho Pass (season 1 had a solid protagonist and villain and they phased out Akane in season 3, thank goodness for that)
- Attack on Titan (despite emoboy Eren, some of the supporting cast was solid, making him bearable)
- Steins;Gate (the main character was totally over the top, but somehow, it didn't bother me as much as in most animes, maybe because even he wasn't taking himself very seriously)
- Lady Oscar ("Rose of Versailles" in English I believe... a childhood treasure for me)
- Claymore (sort of slumped at the end, but still pretty good)
- Cowboy Bebop
- Samurai Champloo
- Fate/Zero (just don't expect faithfulness to the source material they borrow from and you'll be fine)
- Guardian of the Sacred Spirit
- Blood+
Watched some other animes to various degrees (I'm not shy about stopping midway if they give me too much of a facepalm moment) and these are the main ones I'd recommend.
if someone says conservative my background lets me think of Akira, Legend of the Overfiend, Fist of the Northstar, ninja scroll and Robotech and maybe that FF7 movie