Just quit halfway through the first season of my latest anime. It was promising, but got too dramatic and cutesy for me; I skipped to the last episode to make sure my prediction was right, and I don't regret my decision.
On a more positive note, and because I love to hear the sound of my own fingers on the keyboard, I'm going to talk a bit about my anime favorites.

My current short list is, in no particular order:
Miyazaki: Castle in the Sky, Spirited Away, and Howl’s Moving Castle are my big three, as previously mentioned. Nausicaa of the Valley of the Wind, Kiki’s Delivery Service, and Princess Mononoke get honorable mentions.
Psycho Pass: Takes place in a futuristic Japan, where crime has been virtually eliminated by an omniscient system that monitors the 'psycho pass' of each citizen to prevent violent impulses. I can't express how dark, compelling, but ultimately hopeful this show is. Can't wait for season 2 to appear on Netflix!
Darker Than Black Another futuristic anime in which mysterious and 'soulless' people known as contractors cause terror and death. Dark and action-packed, this one is on my list to catch up on once I have more of a disposable income. (The first season appeared on Netflix a while back, then disappeared.)
Death Note: Hey, I mentioned that I'm into dark animes right?
Sword Art Online: A young gamer gets trapped in a new virtual reality MMORPG along with many others in this heroic drama. The premise sounds ridiculous so I neglected watching it for a long time, but I was sooo happy when I finally did!
Knights of Sidonia: A young man becomes the rising star and great hope of possibly the last remnant of humanity drifting through space, many years after Earth was annihilated by incomprehensible aliens. Can't wait for season 2!
Ghost in the Shell: A classic anime film. There's a GitS series on my Netflix queue; not sure if it's a new one or what.
East of Eden: Outside of Miyazaki films, this is the only 'sweet' anime that I've ever fallen in love with. Romance and mystery conspire to create an amazing story in this more-or-less modern world drama.
Arpeggio of Blue Steel: A young sea captain and his crew struggle to give humanity a fighting chance against the mysterious 'fleet of fog' which obliterated all human sea-power more than a decade ago. Somewhat surprisingly, the most defined and dramatic characters are the human-like avatars of the Fleet of Fog's ships, who help and hinder the young captain. Action-packed and fast paced, the first season is very promising.
Angel Beats!: Dead teens live and adventure together in an afterlife with explicitly video-game physics. Again, it's an absurd-sounding plot, but it's strangely compelling; and unlike many drama-focused animes, it has a very satisfying conclusion!
Fate/Zero: Summoned heroes from various mythologies duke it out to win the Holy Grail, a relic capable of granting the victor's master any one wish.
High School of the Dead: A group of high schoolers fight to survive a zombie apocalypse and its aftermath. There's a ridiculous amount of fanservice, but if you can get past that, it's a really fun show.
Fullmetal Alchemist: Brotherhood: Much better than the other FMA: the Painfully Slow One. I probably just POed every fan of the original comic, but hey, I need action! Netflix has season 1 and 2, but not the others for some reason. This is another one to catch up on later.
Ninja Scroll: Sooo did not expect this to be rated R, given its title! Good stuff though, and a classic.
Moribito: A heroic tale of adventure and redemption in a land of swords and magic. Beautiful animation, a strong heroine, a bit of action, and a satisfying ending make this one an instant recommendation for pretty much anyone.
Cowboy Bebop: I liked the film, though I don't remember much about it.
Blood: the Last Vampire: A short and bloody film involving a high school Halloween party, vampires, and a girl with a sword. And that's pretty much all ya need to know.

Not to be confused with the series of similar title and same protagonist, which is much more drama-oriented and slow-paced.
Honorable Mention
Mushi-Shi: Not a riveting series, IMO, but this one is uniquely beautiful. It follows the wanderings of Ginko, a man who can see the mushi; spirit-things that abound in nature, and can sometimes cause problems. The very best soundtrack of any anime I've ever heard, bar none.