Darker than Black

Clannad & Clannad: After Story

Noir

.hack//SIGN (Sword Art: Online's older, less action-oriented bro)

Fullmetal Alchemist: Brotherhood

Fullmetal Alchemist

Fullmetal Alchemist: Brotherhood (Watch after the original)

Gurren Lagann

JoJo's Bizarre Adventure

the puppymonkeybaby commercial on repeat for 45 minutes at a time

Green Hornet, 1940s version.

What, you thought I would recommend the modern garbage? blech.

my favorite anime is king of the hill

my favorite anime is king of the hill

Not nearly as good as Cory in the House.

Also, I totally recommend watching Code Geass.

If you haven't seen the Mentalist, go watch.

I now officially recommend Steins;Gate

El Psy Congroo

Anyway, on the classic side of things, Dragon Ball Z is actually pretty good, if a bit dense (Dragon Ball Z Kai cuts out the unnecessary bits so it's easier to approach).  I also +1 the above recommendation of Fullmetal Alchemist and Brotherhood.

I also want to mention Cromartie High School, just as a possibility.  It's a comedy series trying to be as absurd as possible, so even if you end up liking it it might take a while to adjust.  Another comedy I recently watched and enjoyed was Gekkan Shoujo Nozaki-kun, mainly since it has a meta element to it that I really appreciated, but that might not go over as well for someone new to anime.

And don't watch Gurren Lagann, it's mediocore at best.  The best mecha anime is Brilliant Century Duck Crisis, trust me.

Gravity Falls

Young Justice

Agents of S.H.I.E.L.D.

Agent Carter

The Flash

Princess Tutu

Person of Interest. It's on Netflix and it's amazing, the first season starts out a bit slow but it gets way better. Agents of SHIELD and Agent Carter are also pretty good.

I don't watch too much anime but I really like Kuroko's Basketball. It has some language and other stuff but it's really great.

Mawaru Penguindrum.

Princess Tutu

Actually second this one, it's really good

(Also, FMA, FMA:B, Gurren Lagann, Darker Than Black, and Steins;Gate... and Person of Interest)

*Snaps fingers*