This is a compilation of all of my anime recommendations, in alphabetical order, with a few keywords. (You can also read here.)
A
Attack on Titan: fantasy, BRUTAL, giants vs humans
Azumanga Daioh: high school, hijinks, slice of life
B
Black Lagoon: pirates, violent, mafia, romance, misfit crew
Bodacious Space Pirates: SF, high school, pirates, grrl power, shoujo
Broken Blade: fantasy, mecha, politics, lost civilization, gratuitous boobs
D
Darker Than Black: SF, superpowers, mafia, conspiracy
E
Eden of the East: contemporary SF, college students, conspiracy, hijinks
F
Free!: high school, swimming, female gaze, fujoshi bait
G
Gargantia: SF, mecha, romance, post-catastrophic Earth
Genshiken (Nidaime): college, otaku, hijinks, funny and painful because it's true
Giant Robo: post-apocalypse, mecha, conspiracy
H
Hataraku Maou-sama!: contemporary fantasy, humor, romance, demons vs heroes
Here is Greenwood: high school, hijinks, romance, misfit crew
I
Irresponsible Captain Tylor: SF, comedy, misfit crew
K
Kids on the Slope: historical, jazz, school, slice of life
M
Macross: mecha, pop music will save the day, SF
Mobile Suit Gundam: the 08th MS Team: SF, mecha, gritty, romance
O
Ouran High School Host Club: high school, comedy, queer(ish)
P
Patlabor: near-future SF, robots, cop show, humor, hijinks, misfit crew
Planetes: SF, space junk, humor, romance, hijinks, misfit crew
Princess Tutu: fantasy, high school, ballet, magical girl, deconstruction, fairy tales
Psycho-Pass: SF, dystopian, cop show
R
Revolutionary Girl Utena: high school, queer, coming of age, symbolism
Rideback: dystopian, robots, ballet, college
S
Shinesman: sentai, parody, hijinks, misfit crew
T
Tiger and Bunny: SF, superpowers, humor, family drama, misfit crew
Toradora!: high school, romance, slice of life
V
Victorian Romance Emma: historical, romance, maids, class boundaries
Voices of a Distant Star: SF, romance, short, CG