lista your favourite Anime from each of these genre:

Action - Shakugan no Shana / Sword Art Online
Adventure - Fairytail / Hunter x Hunter
Horror - Vampire Knight
Mystery - Hyouka (somewhat mystery) :P
Psychological - K
Romance - Clannad, Isshuken Friends <3
Harem - Hayate no Gotoku
Reverse Harem - Brothers Conflict
Comedy - Sket Dance, TMOHS (Kamisama Hajimemashite, too)
Romedy (i'd like to add this one) - Special A, Kaichou wa Maid-sama !
Mecha - none
Yaoi - none
Yuri - none

Action-Fullmetal Alchmeist/Brotherhood
Adventure-Fairy Tail
Horror-Corpse Party
Mystery-Vampire Knight/Guilty
Psychological-None
Romance-Kamisama Kiss
Harem-Kanon
Reverse Harem-None
Comedy-Lucky Star
Mecha-None
Yaoi-None
Yuri-None

Action - Shingeki no Kyojin
Adventure - N/A
Horror - Higurashi No Naku Koro Ni
Mystery - Death Note
Psychological - Death Note
Romance - AIR TV
Harem - AIR TV
Reverse Harem - N/A
Comedy - Soul Eater
Mecha - Code Geass *pictured*
Yaoi - N/A
Yuri - N/A

Action: Jormungand
Adventure: Hunter x Hunter
Horror: Ghost Hunt
Mystery: K
Psychological: I don't actually understand what constitutes the definition of a psychological Anime lol
Romance: Too many
Harem: None
Reverse Harem: too many
Comedy: Poyopoyo
Mecha: Code Geass
Yaoi: Junjou Romantica
Yuri: None

I didn't go into major thought about this, so this lista may be a teeny bit inaccurate, but I went with what came to mind.

Action- Black Lagoon
Adventure- FullMetal Alchemist/Brotherhood
Horror- Higurashi: When They Cry
Mystery- DuRaRaRa!!
Psychological- Death Note
Romance- Angel Beats! -pic-
Harem- Kanon
Reverse Harem- Ouran High School Host Club
Comedy- GetBackers
Mecha- Code Geass
Yaoi- none (unless te count manga)
Yuri- none

This lista isn't entirely accurate. For a few of them I couldn't think of any, so I went with one's that I haven't exactly finished yet.

Action-shingeki no kyojin/attack on titan
Adventure-fairy tail
Horror-Elfen lied, another
Mystery-Serial Experiments Lain
Psychological-Death Note
Romance-Kaichou wa Maid sama!
Harem-Air TV
Reverse Harem- none
Comedy-Hetalia
Mecha-Code Geass: Lelouch of the Rebellion
Yaoi-none
Yuri-none

Action- Katekyo Hitman Reborn
Adventure- Magi
Horror- Hell Girl
Mystery- Never seen one.
Psychological- Death Note
Romance- Cardcaptor Sakura
Harem- Zero no Tsukaima
Reverse Harem- Uta no Prince-sama
Comedy- Fairy Tail
Mecha- Never seen one.
Yaoi- Never seen one.
Yuri- Never seen one.

Action- Durarara
Adventure- Pokemon o Soul Eater, maybe?
Horror- Corpse Party
Mystery- Dangan Ronpa
Psychological- Puella Magi Madoka Magica
Romance- Tokyo Mew Mew, I guess.
Harem- The World God Only Knows
Reverse Harem- Ouran High School Host Club
Comedy- Meganebu!
Mecha- Tengen Toppa Gurren Lagann
Yaoi- Don't really care for hardcore yaoi. I did read a cute manga called innamorati Doll though. I may o may not have cried.
Yuri- Yuru Yuri (Technically Shoujo Ai, but I'm not into the hardcore stuff)

Here's mine:
Action-Fairy Tail
Adventure-Fullmetal Alchemist Brotherhood
Horror-Devil May Cry
Mystery-Darker Than Black
Psychological-Code Geass/R2
Romance-Spice + Wolf/II
Harem-High School DxD/Rosario + Vampire
Comedy-The Devil is a Part-Timer
Mecha-Gurren Lagann
Yuri-Queen’s Blade 2: Evil Eye

Action- Bleach
Adventure- Fairy Tail
Horror- Hellsing Ultimate
Mystery- None
Psychological- Death Note
Romance- None
Harem- None
Reverse Harem- None
Comedy- Beelzebub
Mecha- Guilty Crown
Yaoi- None
Yuri-  None

Action: Soul Eater
Adventure: Fairy Tail
Horror: Another
Mystery: Ghost Hunt
Physcological: NONE
Romance: Chobits
Harem: NONE
Reverse Harem: NONE
Comedy: Baka and Test
Mecha: NONE
Yaoi: Sekai-Ichi Hatsukoi
Yuri: haven't seen one yet

Action- Naruto/Naruto Shippuden
Adventure- InuYasha
Horror- Shiki
Mystery- Another
Psychological- Shiki
Romance- Ouran High School Host Club
Harem- Clannad/Clannad: After Story
Reverse Harem- Ouran High School Host Club
Comedy- Cuticle Detective Inaba
Mecha- Code Geass
Yaoi- Junjou Romantica/Junjou Romantica II
Yuri- N/A

Action- Blue Exorcist
Adventure- D.Gray-Man
Horror- Shingeki no Kyojin
Mystery- Death Note
Psychological- Death Note
Romance- None
Harem- The World God Only Knows
Reverse Harem- KamiGami no Asobi
Comedy- The Devil is a Part-Timer
Mecha- Code Geass
Yaoi- None.
Yuri- None.

random thoughts:
Action- Dragon Ball Z
Adventure- Fairy Tail
Horror- Hell Girl
Mystery- Gosick
Psychological- Death Note
Romance- Suzuka
Harem- Tenchi Muyo
Reverse Harem- Wallflower
Comedy- Azumanga Daioh
Mecha- Escaflowne
Yaoi- n/a
Yuri- Yuru Yuri

Action- Fullmetal Alchemist: Brotherhood
Adventure- Hunter x Hunter
Horror- Hellsing
Mystery- Hyouka
Psychological- Death Note
Romance- Kimi ni Todoke
Harem- None
Reverse Harem- None
Comedy- Daily Lives of High School Boys
Mecha- Gurren Lagan
Yaoi- Sekai Ichi Hatsukoi
Yuri- None

Action- Shingeki no Kyojin ~picture~
Adventure- Fullmetal Alchemist: Brotherhood
Horror- Another
Mystery- Higurashi no Naku Koro ni Kai
Psychological- Mahou Shoujo Madoka Magica
Romance- Clannad
Harem- Shuffle!
Reverse Harem- Ouran Koukou Host Club
Comedy- Lucky Star
Mecha- Neon Genesis Evangelion
Yaoi- N/A
Yuri- N/A

Action- Shingeki no kyojin
Adventure- FMA :Brotherhood
Horror- Hellsing
Mystery- Psycho Pass *pic
Psychological- Death Note
Romance- Nodame Cantabile
Harem- N/A
Reverse Harem- Ouran high School Host Club
Comedy- Sket Dan
Mecha- Neon Genesis Evangelion
Yaoi- DRAMAtical Murder
Yuri- Akuma no Riddle

Action- Boku no Hero Academia
Adventure- Magi The Labyrinth of Magic (pic)
Horror- Hellsing Ultimate
Mystery- Death Note
Psychological- xxxHolic
Romance- Ore Monogatari!
Harem- N/A
Reverse Harem- Ohshc
Comedy- Danshi Koukousei no Nichijou
Mecha- Gundam Wing
Yaoi- Amore Stage!
Yuri- N/A