Everyone finds something they like in Cowboy Bebop, so that's definitely worth your time. Someone mentioned Steins;gate, and that's pretty good too, an exciting time traveling thriller with focus on a small group of characters. Not all are equally interesting, but the main character is, so that helps a lot. Gurren Lagann and FLCL are great fun, lighthearted, weird and very dumb with lots of robot action. Eureka Seven had a nice romance set to the backdrop of robots surfing on the wind. So I'll back those.
Someone recommended Soul Eater, Fullmetal Alchemist Brotherhood and Welcome to the NHK, and while those aren't bad, they aren't amazing adaptations and you'd do better to read them instead. Maybe watch some of the fights scenes in the first two, they both did a good job with those. But both Soul Eater and NHK end prematurely and Brotherhood changes some stuff because they made an adaptation years ago that had a very similar beginning and they didn't want to do the same things again.
Neon Genesis Evangelion is pretty great, but has two horrible endings. One in the series, and then a movie sequel as a second ending. They've been remaking it in movies for a while, but that's not done yet, so maybe the third ending is equally as bad.
AC10 said:
Also, try Wakfu. It's french, thus it's not considered anime, but it was a good show IMO.
It's arguably more fantasy, but it's that weird kind of "science fantasy" hybrid style.
I just saw the first season of that show, thought it was really nice. Between Rayman Origins and Wakfu, France has made me believe in Flash animation.