I have a 13 year old friend... (2)

Toradora!
Mayo Chiki
Nisekoi (airing)
Rozen Maiden
Deathnote
Bleach
Angel Beats
Nura: the rise of the yokai clan
Precure
Tsubasa Chronicles
Mekakucity Actors (airing)
Noragami
Lucky Star
Pandora Hearts
Black Butler
Attack no Titans
Sword Art Online
Log Horizon
Princess resurrection
07-Ghost
Kyou Kara Moah!
Shaman King
xxxHolic
Guilty Crown
Air Gear
Angelic Layer
11eyes
Black Cat
Mirai Nikki
Kore wa zombie desu ka?
Fairy Tail
D.N.Angel
Akuma no Riddle (airing)
Kamisama Kiss
Shugo Chara
Mermaid Melody
Cardcaptor Sakura
Tokyo Ravens
Otome wa boku ni koishiteru
Ouran Highschool
Hetalia
Fruits Basket
Squid Girl
Clannad
Mai-HIME
One Piece
Katekyo Hitman Reborn!
Busou Shinki
Kaze no Stigma
The Melancholy of Haruhi Suzumiya

I hope this helps as I watch different genres of anime as these animes, that I listed, are apparently different genres.

Well besides the other anime I listed here's some other Anime I think she would be interested:
1. Shakugan No Shana/2/Final
2. Witchblade {Picture}
3. Neon Genesis Evangelion
4. Nura: Rise of the Yokai Clan/Demon Capital
5. Guilty Crown
6. Aquarion Evol
7. Buso Renkin

So she likes reverse harem?

Ouran High School Host Club
Kamisama Hajimemashita
Uta no prince sama
Inu x boku ss
Saiunkoku monogatari
Kaichou wa maid sama
Special A
Amneisa
Hakuouki
Diabolik Lovers
Fruits Basket
Love Complex
Kimi ni Todoke
Sama Hajimenashita
Hiiro no kakera
Bokura ga ita
My little Monster
Suki-tte li na yo
Hakushaku to Youse
Shugo Chara
Garden Elements
Add just because*
Pandora Hearts
Naruto

Hope she enjoys. ~

Kamigami no Asobi