Ive been using Hulu/Netflix for older episodes and Funimation for new dubs. Im ok with using any of the streaming services, Crunchyroll and Anime Strike besides the ones Ive already used (not sure if there are any others besides these five).
Ok, well, I'm gonna give you some outside the box suggestions to kinda give you some options outside the most recent & most popular shows - this is from a fan of recent and popular shows, but there is a lot more to anime than just fan service and violence, that's what I like about the medium - you can find anything.
Serial Experiments Lain - a somewhat prescient look at the internet and connected life. It's really good, and pretty short.
Aria The Animation - this was recently added to Crunchyroll and just had an Uber successful Kickstarter for Blu-rays. It's a gentle, slice of life anime set on a now water covered Mars. I love Gundam, Attack on Titan, all those sorts of shows, but this is calming and funny and touches a place of nostalgia you don't even realize you need.
Noir - think of Leon: The Professional as an anime, with really good music. It's about a pair of female assassins, their bond, and the conspiracy facing them.
Baby Steps - a sports anime focusing on tennis. I didn't think I'd like it, but it was really good. It's just about a high school kid that gets into tennis and his journey.
FLCL - I have no way to explain this one to you; it's a classic. A sequel is on the way, too.
Sound! Euphonium - it's about a high school concert band, it's good - but displays occasional flashes of brilliance that makes it worth watching.
A lot of what people have listed in the thread are excellent choices, I just wanted to provide some alternative avenues of anime exploration