Here are some shows for those of you who want a good story:
Twin Spica - A story about a motherless younger girl who's dream is to become an astronaut, even though it was because of a space craft accident that she lost her mother. Great emotional story.
Pretty Precess Yucci (puchipuri yuushi) - A story about Yucci, a girl who has stopped growing since her early teens, and her life as she meets four other princess candidates for the princess crown. While the story sounds simple and maybe even childish, it also has a dark twist to it. Overall a very fun show to watch that teaches old fashioned values of anime through a newly animated series.
Niea Under 7 - A story about Mayu, a girl making it on her own through college by working part time, who shares a room with an alien named Niea. Niea is constantly trying to win free food off of Mayu and causes Mayu a lot of trouble. This is probably because Niea is somewhat of an outcast from her own alien community. If you like this, you might want to check out other works that Abe Yoshitoshi has contributed to, namely, serial experiements lain and haibane renmei.
Death Note Comics (not the animated series. Those are really terrible. lol 100% gothified) - One day, example student Raito picks up a black notebook titled the "Death Note". Once Raito realizes the power of this death note is real, he becomes determined to change the face of this world through it.
Last Exile - A science fiction anime about airships and war. Full of plenty of appealing characters (of course, it is Range Murata's characters, after all.) If you haven't seen it, watch it :p
Princess Tutu - a contemporary merge of old time fairy tales and the anime medium. If you're a sucker for fairy tales, tutu is for you.
-- a just shows that I've seen recently:
Jigoku Shoujo (1st season, 2nd season [futakomori]) - :s I dunno. I really liked it. It's a super slow paced anime. If you didn't like NHK ni youkoso, Niea under 7, or Paranoia Agent, then steer clear of this entire series. oh, and see NHK ni youkoso and Paranoia agent, if you haven't yet.
Paranoia Agent is sort of like Lain, but a lot more weirder and none of the zomg internet identity crisis theme)
Rozen Maiden (1st season, träumend (second season), ouvertüre OVA) - A story about an inward boy named Jun and his doll Shinku (or maybe I should have said this is a story about Shinku, and her slave human Jun -__-). Do you like cute anime dolls running around playing and fighting each other? OK. here's an anime for you.
.hack//ROOTS - I've only seen a part of the series, but the music is awesome. Perhaps it's because I follow ALI PROJECT like a cultist.
Lucky Star - The most popular series atm. It's a story about 4 high school girls. Cute School/comedy anime.
Gakuen Utopia Manabi Straight! - What was popular before lucky star. It is also a cute school/comedy anime.
suzumiya haruhi - What was popular before manabi. A conspiracy anime involving a telepath, an alien, and a person from the future.
Ichigo Mashimaro - What was popular before haruhi. A cute comedy anime about four elementary school girls and one [s]high schooler[/s] college age student.
Gurren Lagan - GAINAX (makers of evangelion, nadia, flcl, gunbuster, diebuster; animators of re:cutey honey, karekano, mahoromatic, etc) latest work.