We've seen DearS. The plot goes like this: A flying saucer full of beautiful aliens crash-lands on Earth. The Japanese government gives them a refugee status and after a year, the aliens are ready to integrate into Japanese society. Then, high school student Takeya happens across one of the aliens -- she doesn't speak the language, and sort-of adopts him as her guide (even though Takeya isn't really interested in the physical perfection of the DearS).
It's like Chobits, but much more ecchi. Neneko, the 'girl next door' is actually the most normal character. The teacher is annoying... We don't have to see this one.
Another one we've watched is Kurau: Phantom Memory. Main character is Kurau, a girl of 12 years old. On her birthday, she accompanies her father, an energy researcher, to his work. An accident happens, and she gets infused with weird energy. She... changes, there is some sort of alien presence infused in her body. Fast-forward to ten years later, and Kurau is working as an 'agent', taking all sorts of risky missions. With her super-abilities, she can defeat every opponent easily.
Well, what can I say? Maybe they made Kurau a bit too invulnerable to make it exciting. Also, it's pretty bad SF: 100 years into the future, everything will be the same as it is now (upto using USB-stick-like things to store information), except now we have flying cars? But perhaps there will be an interesting plot later on. klik said 'yes' to this one, I will give it the benefit of the doubt.
Also, there's Otogizoushi. Another samurai-anime, but this time set in the Heian period. There's not much plot in the first episode: all we see is two people (a younge noble and her samurai guardian) questing for a certain jewel and being attacked by raving lunatics who have quite a bit of skill -- presumably the berserkers of the clans that stole the jewel. There is also quite a bit of scheming in the imperial court going on, but, once again, we are not given any details.
Fight scenes are awesomely choreographed, the artwork and animation is top-notch and it breathes an air of history. Certainly one to watch!
Then there's stuff like Girls Bravo... What to say? It's about a short boy who, through repeated bullying, has adverse reactions to... women. Then, when he is bullied by is childhood friend (in his own house, even!), he falls into the bath and emerges again in Siren, another world. There he meets Miharu, a girl of Siren. When she touches him, he doesn't get a rash, which is completely new to him. Unfortunately, there are only very few males on Siren, so when word gets out that Miharu is walking around with a boy, the hunt is up!
What is it with boys falling through the plumbing into different worlds these days? First there was Kyo Kara Maou, now this... All the women are big-breasted, there's lots of casual violence against the poor male protagonist, and there's not much of a plot to speak of. We won't be watching this, naturally.