I think my favorite anime has to be Mahou Shoujo Madoka Magica. I won’t say so much about it, since it’s almost impossible to without spoiling stuff, so… If you try it, just watch until the end of ep 3 before deciding to continue.
The majority of these shows are dark and gritty in some fashion.
-Serial Experiments Lain is also a great psychological thriller.
-Rainbow Nisha Rokubou no Shichinin is a really good drama show.
-Juuni Kokuki is a pretty neat fantasy show.
-Slayers is also a neat fantasy franchise.
-Legend of the Legendary Heroes is a really cool mystery/fantasy series, even though it was never finished 
-Shigurui: Death Frenzy is there for those that likes grotesque and freaky scenes, with barely any filter <~<
-Texhnolyze is a neat dystopia future show. Very slow and artistic, like Lain.
-Apocalypse Zero. I have no idea how to even start describing that. It’s just 4 episodes of pure pandemonium.
Aaaand my favorite romance is… Chihayafuru! It’s so adorable.
I’ve not watched anime in about seven years, so there’s a risk these are a bit outdated and stuff, but yah.