D Gray Man, Naruto, Bleach, Vampire Knight, Hellsing, Claymore, Death Note, Black Butler, Nabari No Ou, Casshern Sins, Dragonaut, Gun X Sword, Strike Witches, Black Blood Brothers, Ghost Hound, Rurouni Kenshin
I'll discuss my favs out of the list:
Out of all these, Vampire Knight has the most romance. The vampires in it are completely hot, but the action/ fighting is light to moderate so far. With the storyline, though, I know there will eventually be some action. People die in Vampire Knight and a girl was already killed in it so far. There is an anime version to watch, but I am reading the manga and am only to ch 34 (there has already been two to three fight scenes, so it is not a strictly romance novel...). It is good enough that I plan on watching the anime too.
Naruto is awesome. If you have not watched it already, do so. It gets even more awesome after the time leap in Naruto Shippuden. It includes shinobis and I would consider it supernatural cause of the "powers' the ninjas have. It also involves demons being sealed inside a few of the shinobi. People actually die in this one too, including main/ fav characters.
I consider D Gray Man the best out of the group. The romance in there is very light to almost nonexistent. However, you would NOT be disappointed at all. The action and storyline is so good it is enough to make you not care about the lightness of the romance. The supernatural elements in this one is heavy and include creatures called akumas who are used as weapons. People actually die in this one too. It is good enough that I am both reading the manga and watching the anime. I'm waiting for the next release on both of them and have yet to be disappointed.
Death Note has romance, supernatural, and suspense. It is more of a suspenseful action cause there is no fighting, but there is a lot of suspense. In this anime, a shinigami (death god) drops a notebook on earth. When a person writes someone's name in the notebook, that person dies. Watch the anime to find out the rest cause it is awesome.
On a side note, you mentioned watching the anime Inuyasha, but have you read the manga? The ending is different. You see, when the anime version caught up to the manga, the director chose to just end the anime instead of doing "filler" episodes until the manga released more chapters. That is why the anime Inuyasha just sort of drops off at episode 167 without any real ending. If you want to see how Inuyasha truely ends, then go read the manga. Start at chapter 355 because that is where the anime ended. The manga ends at chapter 558, so there is over 200 chapters worth of storyline you are missing out on there!
You can read the manga of Inuyasha online at mangareader.com
On an extra side note, I saw the first person mentioned dothacksign (.hack//sign) ... I love that particular anime! I thought it was awesome! But... based on YOUR taste and preference, I don't think you will like it. There is zero romance in that anime and very little action. The anime is mostly the characters talking and the storyline is moved forward, albeit slowly, by their conversations.
years of watching anime and reading manga