Topic: Anime & Manga (NO SPOILERS PLEASE)

Good one to start out with. And congratz, 12 year-olds seem to be the prime demographic of a lot of anime, so there'll be no shortage of good suggestions. I'll start out by suggesting Mobile Suit Gundam (you should be familiar with this from Sgt. Frog) and Full Metal Alchemist. I'd also suggest FMA: Brotherhood, but it's a lot more gorey than the original. It's the only thing I don't like about it.

Because of a certain subplot with a certain mute later on in the first FMA, I question showing it to 12 year olds.

One Piece is the greatest series ever and is the greatest series ever for every age. So, you should read Bleach.
_{hahahaha...don't read Bleach}

I agree. Despite both being amazing animes, and brotherhood being one of the best, I don't think etheir would be exactly appropriate for a 12 year old.

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Hey! I am a know some very mature 12 year olds.
...But you're right. Watch One Piece instead. Because One Piece.

...One Piece.

As do I. But I guess if she was okay with a lot of blood and stuff, she wouldn't be asking for age appropriate shows, so...

Other Anime I Highly recommend:

Mecha:
Zeta Gundam
Gundam X
Macross
Escaflowne

Super Robot:
GaoGaiGar
Gaiking: The Legend of Daiku Maryu
Gunbuster
Giant Robo

Sci-fi:
Outlaw Star
Crest of the Stars/Banner of the Stars
Captain Harlock
Voices of a Distant Star

Fantasy:
Magic Knight Rayearth
.hack//SIGN
El Hazard
Legend of the Legendary Heroes

Action:
One Piece
Dragon Ball
Shaman King
Trigun

Nah, FMA will be fine for 12+ - in fact, that's what it's rated in the UK (and its PG in America). Yeah, there's that subplot, but as it never quite explicitly states what happened (although the dot-joining is hardly challenging) and we never actually see it happen, I think it should be fine. Viewers' discretion, I suppose.
Brotherhood, on the other hand, is quite a lot more violent and gory, and I'd say unsuitable for 12 (I think the rating here for that is 15, actually).

As I'm here, I'll throw in a couple movie suggestions. Drum roll please...

The Girl Who Leapt Through Time and Summer Wars.

Did anyone see that coming? Of course you didn't, shush. _{But really they're awesome and pretty perfectly suited for your age group}
Suggestions that I'm not quite so obsessed about, check out some Ghibli if you haven't done already - Spirited Away, Castle in the Sky, Howl's Moving Castle and Nausicaa are probably the 'definitive' ones, but the remainder of their catalogue is hardly slim pickings - Ponyo, Kiki's Delivery Service, Whisper of the Heart and The Cat Returns are just a few of many excellent films. Grave of the Fireflies deserves special mention - it's an absolutely amazing film, but also amongst the most harrowing. Keep some tissues handy, you will cry.

I'll throw in a recommendation for Steamboy while I'm here too, and the 2 new Evangelion reboot movies (Evangelion 1.11 and 2.22) - they're big and brash and full of giant things going kaboom, but with a strong human story behind it too.

In terms of series... hum, I'm not a huge series watcher. Even of the East is excellent, as is Darker Than Black (rated 15+ here, but I'd maybe put in the 'viewer's discretion' bracket with FMA) and... uh. Now my mind has gone a little blank. Mickey's the man to ask for these things

Rurouni Kenshin, Dragonball Z, InuYasha, Yu Yu Hakusho, Gundam Wing, and G Gundam would probably be good for a 12 year old (at least that's the kind of stuff I was watching around that age).

I strongly recommend Reborn which is my favourite anime. It doesn't really get going until episode 20 but when it does, it is an excellent anime and gets better with every arc. When I say that, that's not including the stand alone episodes in between the arcs as they're mostly fillers. The first 19 episodes aren't though. I also recommend Pandora hearts and Naruto. Pandora hearts could probably be added to the viewer discretion bracket that Vintage mentioned as it can get pretty dark and some of the later Naruto DVDs are 15 so that could go there as well.

You could just watch One Piece. At that point you might not even need a second series to watch.

No kidding. One Piece has pretty much been the only series I've watched for the last four months lol

I'm (finally) almost current on OP, though, so now I have to consider what series are going to fill the sudden vacuum in my anime watching time (I'm thinking Kids on the Slope would make for a nice change of pace, at least - and, on paper, Shinichiro Watanabe, Yoko Kanno and a slice-of-life premise that sounds similar to the amazing BECK seems like it can hardly miss).

Not anime but anyone watch super sentai and Kamem Rider?

I'd just like second everyone else's suggestions (except the Ghibli films, but I know I'm in the minority there), and I'll finish the list I was trying to make earlier, this time including the more not-so-action heavy genres:

Adventure:
Nadia: The Secret of Blue Water
Spice and Wolf

Comedy:
Slayers
Irresponsible Captain Tylor

Romance
Ah My Goddess
Clannad

Drama
Angel Beats
The Third: The Girl With The Blue Eye

Other
FLCL
Tenchi Muyo

wait Slayers IS action filled (thanks to the power of less awful animation it probably has more than most shonen tbh) and isn't just a comedy. Pure nitpicking or whatever but just saying...

Just watch Elfen Lied

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These recommendations are for a 12 year old you know. I'm pretty sure that an anime that has a 17+ age rating on animefreak wouldn't be suitable.

I could be wrong but I think that is one of those anime that is dark and violent because dark and violent is automatically cool, so a 12 year old enjoying it would make perfect sense to me. That's similar reasoning why I didn't immediately recommend the best anime ever, Detective Conan, because it doesn't have much action and is talky and a detective series.

Now excuse me while I hypocritically enjoy Deadman Wonderland.

I was kidding (kind of)

Yeah, but I doubt the person we're making recommendations for would've been able to tell (though I would hope she'd look these up before watching them. As an asside, I didn't look up Elfin Lied beforehand and just started watching it...boy was that a horrifying experience. ).