Action:
-Gurren Lagann
-Full Metal Alchemist: Brotherhood --- The original series is good too, but I prefer Brotherhood and I think overall it is the more preferred series.
-One Punch Man
-Deadman Wonderland
-Jujutsu Kaisen
-Dragon Ball --- I know, some of the animes I'm naming are super well known, especially DB & DBZ, but I just love the original series.
-Black Cat
-Code Geass
Drama/Thriller:
-Steins;Gate
-Monster --- This one could fall under psychological horror, but it's really damn good. One of the few that I still think about to this day. Not easy to find English dubbed, but the original Japanese and a French dub is on Netflix.
-Future Diary
-Danganronpa --- I enjoyed it a lot, but that could be because I also played the games. There's three seasons and the timeline is pretty confusing, especially because there isn't an anime season for the second game. If you do watch it, for Danganronpa 3 you want to alternate episodes between the two seasons, it makes a lot more sense that way. I know that sounds kinda weird, but I'd recommend googling the watch order if you do watch it. It's well worth it, haha.
-Death Note
-Angels of Death
-Perfect Blue --- It's a movie, not a series, but it's very good.
-Psycho-Pass
Horror:
-Junji Ito Collection & Junji Ito Maniac: Japanese Tales of The Macrabre ---- The episodes are sorta hit or miss, much like the source material. But the good episodes are really good.
-Shiki
-Higurashi/When They Cry ---- I prefer the original series, but it's kinda hard to find online, the newer series is good, though. If you can find the original series, I would definitely say give it a watch. It gives a good bit of context to the remake.
-Another
-Tokyo Ghoul
-Elfen Lied
-School Days ---- This one could also fall under drama, since it doesn't have more of the "horror" elements until later on. However, it gets very crazy towards the end. It has some pretty shocking material. I don't want to spoil anything, but if you're sensitive to certain topics, I'd recommend looking online for trigger warnings.
-Parasyte: The Maxim
-Narutaru/Shadow Star --- This is another one where you might want to look up the trigger warnings.
-Corpse Party ---- I'll be honest, I haven't watched the anime, but I've played pretty much every game in the series. Yet another one with some very sensitive/triggering topics.
-Xxxholic
Comedy & Romance & Slice of Life:
-Shimoneta: A Boring World Where The Concept of Dirty Jokes Doesn't Exist
-Ouran High Host Club
-School Rumble
-Lucky Star
-Gravitation --- This one is yaoi (guyxguy), but it was one of my favorites when I was younger, haha.
-Panty and Stocking with Garterbelt
There's probably a lot more that I've watched and am forgetting right now, but hopefully you'll be able to find something out of this list!
I actually had a lot of fun making this, haha.