Some more lesser-known anime you might like

Nadia: The Secret of Blue Water

This series is perhaps most well known for being the anime that *a-hem* "inspired" Disney to make their Atlantis movie. Whether you've seen the Disney movie or not, Nadia is pretty good and well worth watching.
Jean is a young inventor in late 1800s France who meets and helps out Nadia, a young woman near his own age. They are pursued by a trio of jewel thieves (that remind me a lot of Team Rocket) who are trying to steal Nadia's pendant. Eventually they meet up with Captain Nemo (yes, that Captain Nemo) and find the lost underwater city of Atlantis. That's when stuff starts getting real.

Cyber Coil

Cyber Coil was very well received in Japan but as far as I can tell, for some odd reason never got licensed in English outside of Australia. You could call it Ghost in the Shell by way of Studio Ghibli. The show takes place in an city that is acting as a testing ground for experimental augmented reality technology (with the help of special glasses). The protagonists are young kids who hack the augmented reality by taking advantages of glitches that appear, eventually uncovering a conspiracy about what's really going on behind the curtain with with all the AR stuff.

The Adventures of Mini-Goddess

Everybody knows and likes Oh! My Goddess, but this spinoff series doesn't get near as much love. The premise is that sometimes the goddess sisters sometimes get bored and shrink themselves really small, usually having tiny adventures with Gan, a mouse who lives at the shrine and is in love with Belldandy. (Who isn't, though?) These adventures usually end up poorly for Gan.
The episodes are short and silly and a great palate-cleanser if you've been watching something dark or depressing.

s-CRY-ed

At first glance this seems like a fairly generic fighting anime, and while it does employ a few of the regular tropes and cliches, I feel it manages to set itself apart in others. A lot of the superpowers involved are actually quite inventive and there are a ton of great fights. Some of the fights get downright brutal once the fighters involved start running out of power and have to resort to fists.
The setting isn't terribly original: Weird extra-dimensional explosion... yadda, yadda, yadda... people appearing with superpowers... blah, blah, blah... secret government conspiracy... no sé que, no sé cuanto... random dude who never gives up has to fight EVERYBODY.
But, as with most good stories it's not the plot outline that makes it enjoyable but the execution. Most of the characters are likable, there's lots of good character development, and some great intrigue. Highly recommended.

Bamboo Blade

A sports anime following a school's kendo club. There's not much more story to it besides most of them being relative noobs giving it their best and training to do well at the big tournament.
Now, I'm not a big sports anime fan but I was really surprised by how much I liked Bamboo Blade. The characters are interesting and there's a nice balance of serious and silly. There's much more silly than I was expecting, to be honest, but it works to the show's benefit.

Bobobo-bo Bobo-bo

As the title implies, this show is complete nonsense. Really. The picture shown is literally one of the most normal, comprehensible parts of the show. Every scene is a mindscrew and a half and it only gets worse/better/weirder as the show progresses. But if you like absurdist humor, you'll probably love Bobobo.
The background story, inasmuch as it matters, is that Emperor Baldy-Bald has taken over the world and made it illegal for anyone to have hair. Bobobo-bo Bobo-bo is a hero with a huge blonde afro and magical prehensile nose hairs who fights the tyranny of Baldy-Bald. That's the most sense this series makes.
Definitely an acquired taste.

Kamichu!

One morning Yurie wakes up and realizes that she's suddenly become a Kami. So she and her friends set out to discover just what she can do. Along the way she meets spirits, other Kami, and even an alien, all while learning to deal with the responsibilities of being a Kami that people can easily approach for help.
Kamichu feels like what you would get if Hayao Miyazaki had made series instead of movies. This series is incredibly cute but not really in a "kawaii" way. You just... you just gotta watch it. Seriously, put this show at the top of your list of stuff to watch. It's cute, funny, and beautifully animated with historically accurate representations of Onomichi, Japan, circa 1983-1984.

Thanks for making it this far. If you liked this list, you might like the others I've made.
Anime: http://imgur.com/gallery/PDcCS
Non-Japanese cartoons: http://imgur.com/gallery/j15lH