*groans* I hated Death Note. I couldn't even finish it. I didn't like Mirai Nikki that much either, though the end (of the manga) did pull things together nicely and saved the series in my eyes.
I will second the Gundam series. If you enjoy that, you'll probably enjoy
Blue Seed or
Zoids.
You should really watch the Cowboy Bebop series too, and if you go down that path (along this path is also Trigun)
Outlaw Star is a good place to continue, and
Noir.
Then of course there's the lighter side of anime with
Dragonball (not Z),
Lupin III,
Sailor Moon (also, original is what I'm referring to here),
Pokemon...and so on. I kinda call this (along with
Inuyasha and
Rurouni Kenshin) the "roots" of anime, because it was the first presence I saw of it in the states and it presents a lot of the quintessentials of mainstream anime.
Then there's the blow-your-fucking-mind experimental animes out there. I seriously and strongly suggest everyone who wants their mind blown to see
Serial Experiments Lain. It helps to put this anime in the this frame of mind: it was made in 1998, Futaba Channel was founded in 2001, and the 'hacktivist group anonymous" was...what, like 2010? It will blow your fucking mind this anime will. Also in this category is
Blame!I don't really watch that much anime, but I hope this somehow helps.
Honorable mentions:
D.N.Angel and
Fruits Basket. I didn't see much of D.N.Angel, but what I did see I liked. AND FRUITS BASKET IS SO CUTE
I'M GOING TO GO WATCH SOME NOW.