I'm currently too lazy to make a big gigantic post so here are my favorite anime (in order of descending preference)
Haibane Renmei: Ok some of the other anime I'll post are kinda "guilty pleasures," like my brain acknowledges that they're kinda trashy and not that special but I just love them anyway. Haibane Renmei is the complete opposite of this. No guns, no boobs, all thought. This is a thinking anime, that you have to pay attention to while watching, that explores themes like redemption, loneliness, the meaning of life, etc. The whole universe in which this anime takes place in is a microcosm of our existence, and it's really beautiful to watch unfold. The more you think about and the more times you re-watch this anime, the more genius you'll uncover. There are other thinking animes I guess, but this one is my favorite because I really do agree with all the answers they come up with. It's only 13 episodes and it is just absolutely stellar.
Mushi-shi: This is a really fascinating show that is set in like pre-modern Japan but with an interesting twist; strange little creatures called mushi. Probably related to the kami of Shinto lore, mushi are the essence of all life and are kinda difficult to describe so im going to stop lol. Again, no guns, no boobs, and only one or two episodes of real violence, but this show is visually stunning and in each episode presents a different story of sorts. It's a really unique show thats difficult to describe, but it's like every episode some old Japanese dude sat down next to you and told you a different story of Japanese folklore. Really fantasitc, unique show.
Kokoro Connect: This one is more on my "trashy" end of the spectrum, I just finished watching it and it was LOVELY. Toradora! is kind of a better version of this, but I just personally couldn't enjoy Taiga as a character so, while I really loved the show, it never really got me. This show is more SOL-y, yes, but still very dramatic and with really refined, believable, engaging characters. There's good drama, fantastic animation, a very catchy OP and pretty good character development on all fronts. Not a unique show, surely, but a great one. After watching this I really want to watch Hyouka next, but the FINAL FOUR EPISODES OF KOKORO CONNECT COME OUT ON DECEMBER 30 so I have to wait until then.
Princess Mononoke: Yeah I have a movie on here what about it? Another Miyazaki movie, yes, and while I haven't seen too many I feel like this must have been his greatest. It's about the environment and nature and it's balance with humanity, and it explores these concepts by, like Mushi-shi, re-introducing some shinto-ist elements like spirits and kami. I think, like most Miyazaki movies, that it's a great coming of age story, and I love all the visuals in it. Good flick.
Angel Beats!: Again, closer to the trashy end of the spectrum but I still really liked it! It's like a mix of Clannad and Haibane Renmei for me, and while most of the characters aren't anything special, I really enjoyed the premise of the show and the story that I watched unfold. There was some FANTASTIC drama in the show, and the last episode was just heart-wrenching; it's the only show that has ever made me literally gasp, all while trying to hold back tears and then just being reduced to sobbing. It's worth the 13 episodes imo.
Clannad After Story: I think this show was kinda limited by its being based on a visual novel and having to go through all of the other routes and such like; if it had just been Nagisa and Tomoya from beginning to end, while possibly developing other important characters like Sunohara and some of the other chicks to some degree non-romantically, it would have been a lot more touching and beautiful than it already was. Some flat characters, definitely, but still a really precious storyline. Episode 19 of Clannad After Story made me cry like a little bitch[EDIT: maybe 18? the one with the robot in the field], and if you didn't then I don't know what else to tell you. Is it overhyped? Yeah, probably, but it has some of the best production values of any animation in history and a beautiful storyline so just go watch it.
5 Centimeters Per Second: Yeah this show's animation was so good that it makes real life look unrealistic. Let me rephrase that. After watching this show in HD quality, I looked around my room and was wondering why the resolution was so bad. The animation is really good. Combine that with a touching and realistic love story, and this is worth the 72 minutes of your time it will require you to watch this masterpiece.
Usagi Drop: This show is just heartwarming. The manga got REALLY weird after a certain point (or so I'm told) so I'm glad the anime stopped before that, but it's just a story about a middle aged man who adopts a 5 year old girl who nobody else wants. How cute is that? The girl does cute stuff and the gruffy dude turns out to be a great dad and it's charming and I love it.
Welcome to the NHK!: Probably the only show I've watched that where I really enjoyed every OP and ED. This is a somewhat dark show, but I think it's really valuable, and it hits home pretty strong for a lot of us who think they spend too much time on the computer pissing their lives away. Most people have seen this so I won't go too in-depth but go watch it if you haven't, it's a classic for a reason.
Baccano / Durarara: pretty comparable shows imo, the strengths here are the stream-of-consciousness style of storytelling, really great characters, and an intricate and engaging plot. One explores mob life in the 30's, one explores urban gang life (to some extent). Have you noticed how my descriptions are getting shorter and shorter lol? It's like I'm writing RMTs again. You'll fall in love with the characters and be entranced by a plot you don't fully understand until the very end, all with some great action scenes. Good shit.
Kino's Journey: Another thinking anime, but probably just a tad too artsy. Kino is a great character and Hermes is a pretty all right straight man, and together they go on an adventure and explore the world and learn about different cultures and ideologies. Every episode has a life lesson of sorts, and you can agree or disagree with what they say but it's still valuable, I think. My brother thinks they bite off a tad more then they can chew sometimes, and I'd say that's a valid criticism, but I still really like it.
edit: wow that turned out pretty gigantic anyway