A little help please!

Anime which contain a little bit of each of these genres are "Kamikaze Kaitou Jeanne" and Tsubasa Chronicle".

Fantasy/Drama/Psychological: Puella Magi Madoka Magica
Romance: Toradora (?)
Adventure: Akira (movie), Mirai Nikki (warning: both of these can get kind of graphic)

I think Black Butler / Kuroshitsuji has all of the specified genre, except Romance ;) But it's the BEST Anime I knew! <3

all

Here are a few I like!

Black Butler/Kuroshitsuji (I'd consider it a mystery/drama)
Death Note (Mystery,Drama and probably adventure is well)
Angels Beats: Romance/adventure I think. It was short and pretty good!

Romance anime genre for teen is Oregairu,Special A Class,Zero no Tsukaima,Kamisama Hajimemashita,Chibi Vampire Karin,and Ouran High School Host Club.

Hakushaku to Yousei
InuxBoku SS
Kamisama Hajimemashita
Sword Art Online
Myself; Yourself
Ao Haru Ride
Special A
Hanasakeru Seishounen
Ghost Hunt
Saiunkoku Monogatari
Skip Beat!
Itazura na kiss!

I recommend True Tears, Hanasaku Iroha and Nagi no Asukara (Fantasy), which are all Drama and Romance anime. Tari Tari is also a good Drama, although it isn't listed as one anywhere I look (there isn't any romance is this one, but there are hints of it between two characters).

Natsume Yuujinchou- All time fav anime; fantasy, adventure
Psychic Detective Yakumo-Mystery, adventure, drama, romance
Persona 4- Mystery, adventure, fantasy, hints at romance
Zombie Loan- Drama, mystery, adventure, hints at romance
Brothers Conflict- drama, romance
Wolf's Rain- Adventure, mystery, some romance
Eden of the East- romance, mystery, drama
Zetsuen no Tempest- Adventure, romance, drama, mystery

And the list could go on and on... really I think all the anime out there has at least something on your list now that I start thinking about it lol. I agree with who ever said that above. I just listed some of my favorites that had combinations.

Pictured is Psychic Detective Yakumo... I think it has all of those genres. Also Zetsuen no Tempest has all those too.