Girly one: Card Captor Sakura
About a young girl who finds out she's the descendant of a great magician, who empowered a deck of cards, which are now running rampant, so she has to capture them. Her friends are one bi-curious young boy, her big brother's friend who she and that boy have crushes on, and her classmate (girl) who is arguably in love with Sakura and makes her costumes to fight cards in.
Uncomfortable one: Chobits
There are computers in the world who take the forms of robots, of course, pretty girl robots. Some people love and marry theirs, but can robots love you back? This show is good, but makes me cringe a little and makes me uncomfortable. Still watched it twice.
Recently watched: Deadman Wonderland
It's freaky, main plot is explained in first episode pretty much. But a young guy is convicted of a crime he didn't commit, and sent to this new private prison (Deadman Wonderland) where they battle inmates in games etc.
Re-watched (3 times): Hunter X Hunter
Friendship, fighting, power-ups, and a great story.
Ongoing one: One Piece
Shonen pirate-show about authority and justice, and a government that's burying the "real history" of how it came to rule the world. Also fighting and power-ups.
Old-time japan one: Samurai Champloo
Girl saves two samurai who are each others opposites, one is very calm and proper and the other is impulsive and rude. Then they follow her on her journey to find a samurai who smells like sun flowers. Quirky but keeps a good story, with cool sword fights.
Based on a game: Ragnarok
Based on a top-view clicky-MMO, that I believe came from Korea? Not sure. Follows the hero - a male warrior-class, on his adventure towards the final boss. Together with his female healer-class friend they meet a greedy merchant girl, a sexy mage woman, a sexy archer woman, and I think there was some warrior-class mentor to the main character who had a higher lvl warrior-job class. A fun watch for MMO players perhaps
Romantic one: Kimi ga nozomu eien (The eternity you wish for/Rumbling hearts[alternative titles])
Boy meets girl, things get complicated, much drama ensues.