Yu Yu Hakusho:  (a.k.a. Poltergeist Report) One day, a teenaged punk named Urameshi Yusuke dies in a freak car accident,saving the life of a stranger in the process.  But that's only the beginning.  Yusuke is given a second chance at life, if he can manage to get his act together and convince someone back among the living to give him a hand...
Then, once he has that accomplished, Yusuke is presented with the bill: he is now a spiritual detective, traveling around fighting demons, recovering stolen spiritual artifacts, etc.  Of course, even his recent experiences haven't stopped him from acting like a total jerk...^_^
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Chibis of (top to bottom, left to right): Hiei, Yusuke, Kuwabara, and Kurama. =^_^=
Characters:
Urameshi Yusuke
Botan (the Grim Reaper)
Kuwabara
Keiko
Kurama
Hiei
* Eyecatch = the images shown to get the viewers' attention back after a commercial break.
Who doesn't enjoy the occasional fistfight?  When I think about this show, I think of Dragonball Z, except with a plot (I love Gokou, Vegeta and Mirai Trunks, too, but you know I'm right ^_^), and less in the way of watching characters "powering up," rolling around on the ground moaning, etc.; the fight sequences are actually pretty good, and fairly original..  Plus, it's another show with a decent dub, like Cowboy Bebop.  I didn't like it at first, but it's slowly growing on me, mostly because it has a great sense of humor, and has no problems taking the main character down a peg or two.  Plus, the eyecatch* has cute chibis** of all the main characters; how could you not love that? ^_^
If you're a nonviolent person (meaning that seeing junior high-aged kids getting the crap kicked out of them disturbs you, or you have a little kid in the room), I wouldn't reccomend this one to you.  People get beat up pretty badly in this show; nowhere near as much blood as in, say, Cowboy Bebop or Battle Angel, but a lot more punches and kicks flying around.  Again, it's a lot like DBZ, but with more realistic injuries and damage.  Definitely not  the most violent I've ever seen, though (Gally and Spike pretty much have the corner on that market).  Only the part where that demon is mashing all the bones in Kuwabara's arm one by one has been really distressing so far...
P.S. If you've ever wondered what "shounen" anime is, look no further.  It doesn't get anymore shounen than this!
** Chibis = "chibi" literally means something along the lines of "superdeformed;" usually a small, cute version of an anime character
Metal Angel Marie:  (a.k.a. My Dear Marie)  "Ever meet the perfect girl?  Did she have the perfect boyfriend?  Feel like you can't compete?  Why not build your own?"
Sound crazy?  Well, don't worry.  It is. ^_^  Hiroshi, a nerdy engineering student, has a colossal crush on Mari, another student at his college.  He takes the same classes she does, and joins the tennis club, all to be near her.  The only problem is, she's already got a boyfriend, Tanaka (or so
Tanaka says...)
So Hiroshi decides to build his own Mari.
Everything's going great, and the android Marie is working fine, until Hiroshi forgets his tennis racket one day, and she decides to take it to him at the tennis club...
"...Marie has a mind of her own and a whole host of questions to go with it.  The same questions that each of us ask of life.  Where did I come from?  Why am I here?  Why do I look just like that girl over there?"
Mari (human)
Marie (android)
Characters:
Hiroshi
Mari (human)
Marie (android)
Tanaka
Hibiki
Hibiki
Hiroshi
I cannot reccommend this one enough if you like romantic comedy!  I actually snorted milk out of my nose, and it's the best English dub I've ever seen.  Why, oh why, are there only three episodes?!?! :(
My very first impression, honestly, was "
What the...?"  Then I started laughing, and I didn't stop for a long time.  It's a show that just sounds messed up and crazy, and then you watch it, and it is...but it's also hilarious, touching, and a little bit naughty. =^_^=
My very favorite part is the chibi Marie that introduces each new episode.  She looks a lot like one of the chibi Washuus from
Tenchi Muyo!, but she has her own very distinct personality.  (She's the one that made me snort the milk, btw...)

Just a little note: this one's not for kids.  It contains some adult themes, plus they might get a little bored since there isn't much action.
Bishoujo Senshi Sailormoon
Gundam Wing
Cowboy Bebop

Card Captor Sakura
Digimon

Metal Angel Marie
Yu Yu Hakusho
Bubblegum Crisis Tokyo 2040
Magic Knight Rayearth
Tenchi Muyo!
Inu-Yasha
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