My girlfriend had the anime dvd set of The Melancholy of Haruhi Suzumiya Vol. 1; so we got to watch it last year.
The story stars Kyon, a normal high school student in Japan.
He crosses paths with Haruhi Suzumiya, a classmate who's bored and quite strange. She says the only thing she wants is to meet aliens, time travelers, or espers.
They then meet Yuki Nagato, a bookworm who almost never speaks, and when she does she seems inhuman. She turns out to be a non-organic alien from outer space.
Mikuru Asahina seems to be a very shy and nervous girl and high school student. She turns out to be a time traveler from the future. She also gets to dress up in hentai-inspiring costumes.
The last of the main team is Itsuki Koizumi who turns out to be, you guessed it; an esper. He can only use powers in certain times and spaces so he is mostly a goofy weirdo who worships Haruhi for one reason. Him and his group of espers believe she is the being most cultures refer to as God. This turns out to be true, though Miss Suzumiya doesn't realize it.
The show can go from goofy to serious in a heartbeat. It's actually quite good with lots of humor, good storylines, and a very uniqueness to it. Defiantly check it out if you can.