It's difficult to describe the story without giving too much away. Suffice to say that it's set in a school and focuses on the efforts of Haruhi Suzumiya to keep busy. It's presented in rather a strange way but stick with it and you'll really enjoy it. You could go looking it up on wiki but it's best not to if you want to get the most from the series.
And if that's not enough, this website catalogues many animé series that you can find on YouTube. I started watching Elfen Lied which is pretty much one of the goriest things I've seen since Kill Bill, but then it gets all cutie. The intro which is a melange of latin prayer, klimt paintings and naked elf chicks is definitely not for a Mid-Western audience.
But then that's animé.