From what Netflix has Samurai Champloo is about the best, but it is also one of the best anime titles ever, so that is not too hard.
Trigun is not bad but much more lighthearted than Samurai Champloo.
Mushi-Shi has a very good, serious mood, but doesn't really go anywhere. Give a few episodes a try, and when you lose interest, feel free to stop.
High School of the Dead is short and fun, but also really, really dumb. Turn your mind off and enjoy.
Eden of the East was well-liked by some people, but after the first two or three episodes I completely lost interest.
I feel like Shiguri Death Frenzy is a criminally underrated show. It is about two samurai building up to a fight with each other over 13 episodes. It is super dark, but I really liked it.
If you want to watch anime, listen to the people here and get a crunchroll subscription.
If you're not into anime that much but want more than what Netflix offers, get Hulu Plus. It still adds about two titles a week, and there is a lot to like. Attack on Titan is a fantastic modern show. You can also watch Lupin 3rd: A Woman Named Fujiko Mine, which is pure style. Also, Hulu has been adding a lot of British programming recently that is not on American TV, and it has other international shows. I'm pretty close to canceling Netflix, but Hulu will not be going anywhere, they just add too much content.