Pixy went and challenged his audience to come up with a ten-most-representative list of anime from 2000-2009. First off, in order to come up with these representatives, you need to come up with proper categories for the period under consideration. Und so:
1) Magical Girl
It's debatable whether the Oughts were a good decade for Magical Girl. It's a shoujo category (aside from seinen parodies - see next catagory), and shoujo anime's had a bad, no-good, limping lame decade. The resources have been mostly sucked into otaku rubbish, and fujoshi are a distinctly minor and incidental audience for the anime studios. Furthermore, fujoshi couldn't care less about magical girls. There's something distinctly Showa or early Heisei about traditional mahou shoujo. As the decade wore on, the magical girl show went somewhat sideways - becoming increasingly baroque, odd, or just plain decadent - notable examples include ballet fever-dream Princess Tutu, the slow and cheerful-doomed fatalism of In Search of a Full Moon or the impenetrable, gnomicly endless Pretty Cure franchise. So, creeping in just under the 2000 start-line, I'm going with the final word in old-school magical girl, CLAMP's Card Captor Sakura.
2) Magical Girlfriend
(note, these are completely distinct and mostly-unrelated - see My Wife is a Magical Girl for exception to rule.)
Magical girlfriend, unlike magical girl, is a masculine, otaku-ish wish fulfillment genre - a literal Manic Pixie Dream Girl descends upon nebbish protagonist & makes him into a man. Our heroine is some sort of magical being - goddess, devil, fairy, ghost, etc, etc - who for whatever reason, appears to live with protagonist & make his life wonderfully awful. These are endless, and so forgettable that you find yourself forgetting the details before the DVD stops spinning in the drive, but notable examples include Crazy Shrine Maidens Kannagi, Steel Angel Kurumi, Mahoromatic, and an absolutely endless parade of their peers and lesser lights. This one has to be the Melancholy of Haruhi Suzumiya, wherein our protagonist discovers that God is a petulant, bored high school girl who must be entertained upon pain of Armeggedon; think of it as Kierkegaard in a moe moment, Fear and Trembling before the Demiurge in a sailor fuku.
3) The Reverse Harem.
Traditionally, the harem show is male-oriented, but the Oughts saw an influx of harems full of bishounen for the ladies, as the fujoshi cannibalized what remained of the dying shoujo anime market. And we saw a bunch of good ones, such as Pretear, Ouran High School Host Club, and the Wallflower. But as good as those shows are, the rose has to go to the original reverse-harem - 2001's Fruits Basket.
4) Juvenile Delinquents
We don't tend to see many of these over here, because the art-style is generally ugly, the sentiments rather barbaric, and the comedy brash, brutal, and kind of insular. But there were a number of these which worked pretty well in the Oughts - the yakuza-schoolteacher school comedy Gokusen, the magical-girlfriend fusion Midori's Days, the thugs-and-Freddie-Mercury-do-Azumanga Daioh comedy Cromartie High School, and even the much-maligned street-fighting comedy Air Master. But the show to watch in this category is 2002's Tenshi na Konamaiki, whose manga was released in the states by Viz under the name Cheeky Angel. Yeah, I was just saying over on AoD that there isn't a chance in hell of it ever getting licensed in North America. I don't care, it's funny as all heck.
5) Real Robot mecha
There are generally two types of mecha shows, semi-realistic "robots are pilotable tanks", and the broad-wild-crazy "robots are Gods Upon The Earth". This is the former, and as it sounds, it tends more towards the realistic. Mecha doesn't really go out of fashion, but sometimes the fashions take certain fans out of what they're doing in Japan at the moment. I thought about giving this palm to Kyoto Animation's Full Metal Panic: the Second Raid, but that show's a sequel, and its original just didn't have the steam to bring a new fan into the spirit of the thing. So I'm going to go with the glorious, mad, Lord-Byron-beautiful Code Geass, which took an alternate-universe political soap opera, filled it with roller-blading mecha, and put a swanning teen-aged Magnificent Bastard anti-villain at its manic core.
6) God Robot mecha
And while we're on the subject of the two types of mecha, here's the other side of the coin - the giddy, testosterone-poisoned God Robot genre. The Nineties were a better decade for God Robots than the Oughts, what with Evangelion, Rahxephon, Neo-Ranga, and the like, and I could have been convinced to leave this category out for lack of good examples; the only specimens were dripping with irony and the stink of sweaty fanboy parody.
Then Gainax made Gurren Lagann, and all of a sudden we're in the midst of a minor Go Nagai revival. Hot-blooded raging giant robots are back, and they've beaten irony to death with the backside of a ten-ton drill.
7) Psychic Fightin' Teenagers
Now we come to a genre I don't have much use for - Naruto, Tokyo Underground, Tokyo Maijin, Bleach, etc. I thought of going with A Certain Magical Index or its yuri-iffic sequel A Certain Scientific Railgun, but they're neither particularly good nor particularly representative.
Psychic Fightin'Teenagers shows are kind of eh, but it's the sort of eh which people - other people - love the heck out of. But, I do have a fondness for the Bleach manga, and I discovered last year that my father watches it on Cartoon Network. That's enough to pull you out of the pack of shounen jive, Bleach. Congrats, you suck a little less than your peers!
Moe is ineffable - to define it is to kill it. I am ashamed to admit that I watch far more of it than I'd like people to think, because it really does sail way, way too close to lolita-complex skeeviness. The Oughts are pretty well dominated by the Reign of Moe, from Azumanga Daioh to Lucky Star to K-On!
I'm tempted to be obnoxious and cite the killer-loli slasher-moe that I'm watching right now, When They Cry, but it isn't all that well-animated, and really, why go for the shock value? So I'm going to grab for something from Shaft and Akiyuki Shinbo, the King of Moe. It has to be Hidemari Sketch, a completely and utterly platonic ideal of moe.
9) Kung Fu, Gun-Fu, and Contemporary Hardasses
Criminals, kempo masters, cops, and gunsels - there's a lot of this going out there; Nabeshin when he's being all serious and calling himself Shinchiro Watanabe is a past master of this sort of thing - see examples like Samurai Champloo, Michiko and Hatchin, and Cowboy Bebop. But this decade's most essential gun-fu calvacade of badassery is Black Lagoon, with its black-and-coal-black morality, corrupted view-point protagonist and his Ax Crazy/Heroic Sociopath kidnapper-slash-love-interest. It really is essential viewing - just don't watch it with children in the room.
10) Weaponized Women
Girls with Guns is *so* Eighties. The Oughts' innovation along these lines have been crudely called "Pokegirls", but I prefer the old gag translation of Saikano, "Weaponized Girlfriend". Sometimes it's literal, like the fighter-plane-legged heroines of Strike Witches, sometimes they're mutated escapees from the magical girl ghetto like Nanoha, and sometimes the badassery is bionic and all on the inside, like Kiddy Grade, but mostly it's cute girls with the individual destructive capacity of a mid-range Third World Military and the aerial agility of aerobatic stunt squadron pilots. This one is definitely going to be One Maiden Army Corps exemplar Mai Otome.