You will all hate me after this...
Anime; after listing some, I realized that I haven't watched/finished most of these. They are, however, interesting and I won't recommend anything I don't know some things about - seeing an image, listening to a song, etc., are things won't count to "some things". Basically if have seen many clips or read a whole ton on them, then I will recommend them:
Clannad (I haven't finished this)
Hyouka
Technolyze
Samurai Champloo
Cowboy Bebop
Ruruoni Kenshin (I remember watching some of this)
Angel Beats (Have not watched; just seen clips especially the funnies and the sad parts)
Berserk
Yu Yu Hakusho (Yay, childhood memories!)
Welcome to the NHK (This changed my life, man! You don't know! You know nothing! *foams from mouth*)
Minami-ke (Don't ask why or how; I just find it heartwarming and funny)
Tamako Market (See above)
Speed Grapher (Haven't seen it; read stuff about it; I find it interesting)
Monster
Ergo Proxy (People mentioned this a lot when they were discussing Texhnoloze)
Sankarea (It has an unique take on zombies)
Hellsing
Chunnibyou Demo Koi ga ****ai aka Love, Chunibyo & Other Delusions
Dusk Maiden of Amnesia (I don't remember how I came across this)
Seitokai Yakuindomo (If you like innuendos left and right, then this might be for you)
Danshi Kokosei no Nichijo aka Daily Lives of Highschool Boys (It's funny; trust me)
Baccano
Durarara!!
Ghost in the Shell
Darker than Black
Spiral
Case Closed
Multiple Personality Detective Psycho (The title alone lets you know this is a really messed up and disturbing anime. I'm scared of even watching or reading it)
Dragon Ball (Obligatory)
Kurozuka (Something about vampires, decapitation, and the quest for an immortal loved one)
Kami-sama no Memo-cho aka Heaven's Memo Pad (It seems interesting with people solving crimes and whatnot)
Yami to Boshi to Hon no Tabibito (It's a yuri anime where a girl travels across worlds to find her adopted sister who turns out to be something "celestial". Don't judge me)
Devil May Cry (Why the hell not?)
Claymore
Black Lagoon
Steins;Gate
Manga; pretty much anything I listed would be okay except for Welcome to the NHK and Texhnolzye which was an original anime series; there was no manga to begin with. Welcome to the NHK is weird. At first it was a novel and some of the more "sensitive" things were taken out when the anime was made. The manga is an adaption that deviates from the novel especially with the ending and the personalities of the characters, however, that doesn't change the messages Welcome to the NHK is trying to get across, but it does make a main character seem "off" compared to the novel and anime.
Original Video Animations/OVAs and animated films:
Sword of the Stranger
Any Studio Ghibli film
The Girl Who Leapt Through Time
5 Centimeters Per Second
The Place Promised in Our Early Days