Darker Than Black (this one’s a bit newer than the others I mentioned, it’s one of my favorites though, lots of action and mystery)
Rurouni Kenshin ( old but really good, it’s in the meiji era so lots of sword fighting)
Wolf’s Rain ( so awesome and a bit sad and it has a great soundtrack!)
Yu Yu Hakusho (fantasy, it’s old but a great series)
Stein’s Gate (more of a thriller/mystery, I’m still watching it and the more you watch the better it gets. you have to pay really close attention though)
Deadman Wonderland
Oh Berserk, I almost forgot! (berserk and deadman wonderland are both on the mature side though, so I don’t know if you like that kind of stuff, but I’ve watched both and they’re awesome! here’s another more mature one, it’s Gantz, by the way I suppose these are all on the fantasy side)
Shiki, this is a horror type anime, it’s one of my favorites and I’ve actually been meaning to watch it again!
Another (another horror anime, it’s addicting for only 12 episodes I’ve wanted to rewatch this one as well)
Attack on Titan, but I won’t even suggest this one really, I mean who hasn’t heard of it. Personally I’ve watched it and I really like it but all the hype around it can really you not really feel like watching it, but it’s just as good because it is different