I sent a suggestion list to Stormheart with gifs and descriptions of each show. I figured that I might as well post it here too, in case we have any unregistered lurkers or a user here that is on the fence about one of the anime I listed/doesn't know what to watch next. I'm working my way down starting with my favorite to my sixth favorite.

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WataMote (A.K.A. WATASHI GA MOTENAI NO WA DOU KANGAETE MO OMAERA GA WARUI)
My favorite anime and show. It's about a 15 year-old girl (Tomoko Kuroki) who suffers Social Anxiety and therefore struggles to communicate with other people. The series is about her attempting to overcome her Social Anxiety and her day to day life. She usually comes up with plans that make sense based upon what she observes, but usually backfire. This is a Spice of Life/Comedy and is arguably even a study of Social Anxiety, some people have called the show tasteless and cruel, but I, a sufferer of Social Anxiety, love it.
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Toradora! (A.K.A Tiger Dragon)
My second favorite anime, it was my favorite for a very long time until WataMote came along and dethroned it. Toradora! is about a boy (Ryuji) with eyes that usually causes people to fear him (much to his dismay) and a cute girl (Taiga) with a serious attitude. The two soon discover that they like each others best friend and form an unlikely alliance to try and end up with them. This is a Spice of Life/Comedy/Romance/Drama.
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Spice and Wolf (A.K.A. Ookami to Koushinryou)
One night a travelling merchant (Kraft Lawrence) comes across a surprise in his cart, nestled asleep inside is an attractive nude woman with wolf ears and a tail. The woman identifies herself as Holo, the wise wolf. The two eventually reach an arrangement and begin to travel together. During their travels Holo begins to demonstrate a deep understanding of economics, much to Lawrence's surprise. Is the travelling merchant in over his head? Will he be outfoxedwolfed? You'll have to watch this show about Economics/Romance to find out.
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Daily Lives of High School Boys (A.K.A Danshi Koukosei no Nichijou)
Daily Lives of High School Boys manages to keep things fresh by featuring a wide array of characters and glimpses of their lives. It's a very Robot Chicken-esque show, that is to say random, but random in a way that makes sense and pertains to the lives of the High School kids. It sets up many long running gags and even breaks the fourth wall on occasion. DLoHSB is pure comedy (and fun).
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Clannad and Clannad: After Story
Clannad is about a High School delinquent (Tomoya) who cuts class and a girl (Nagisa) who dreams of bringing back the theater club. The two meet on the way to school one fateful day and set out to bring back the theater club, which might not be as possible as they had previously thought. Clannad is a Romance/Comedy/Drama
Clannad: After Story covers Tomoya's life after High School and deals with him becoming an official part of society. He soon learns that the life of an adult isn't necessarily a glamorous one and experiences may vary, as trials begin to line up to test his resolve. Clannad: After Story is known for tearing viewers down and bringing them to tears (don't google image search Clannad as you'll be spoiled). Clannad: After Story is a Romance/Spice of Life/Drama
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Angel Beats!
A main character with a severe case of amnesia, a student taking aim at the student president with a sniper rifle, and awesome music is what one is immediately treated to when tuning into the first episode of Angel Beats! Guns blazing on the High School grounds is an everyday occurrence in Angel Beats! Angel Beats! has a unique premise, one which will be clear by the end of the first episode. Can the amnesiac regain his lost memory and who will he ultimately side with? This anime is a Drama/Mystery/Fighting/Comedy.