I've been reading Yoshiyuki Sadamoto's manga version of NGE, and while I find it a little more palatable than the what I've seen of the anime, I can definitely understand why so many people hated Gainax for what they did with it. I'm not too fond of them myself because they made the ending so damn confusing. And now they're doing a "remake"...
I've always been drawn to the more thoughtful anime shows/movies out there (I'm working my way through both GITS: SAC and Paranoia Agent and I'm loving it) - my other favorite movies are Patlabor 1/2, Metropolis, and Paprika. The Wings of Honneamise (and it's a travesty that more people don't know about this film) is one of my all time favorite films, along with Tekkon Kinkreet (yes, I know the manga is supposed to be a lot better than the movie). Jin-Roh: The Wolf Brigade and the Macross Plus OVA was really good, too. I kinda like the original GITS and Akira, but in both cases I found the ending to both sort of disappointing (any opinions on GITS 2: Innocence?).
LordCinnamon: Deathnote is very good if you just stop watching after episode 25.
My opinion of this is mixed; I for one really liked the new plot arc with Mello and Near, but I was disappointed that they didn't give any of them nearly as much attention as L, which I didn't think was fair since both characters could have been just as interesting as L was. Before episode 25, the show felt balanced between Light and L; afterward it felt like Mello and Near were just dropped into the show just to give Light someone new to fight. It all came across as being way too rushed.
And I have to confess, my guilty pleasure is Macross Frontier. It's loud and mindless, but I have to forgive its many sins for the sheer awesomeness in episode 7 and in episode 25. On that note, I really like Macross Zero, too - the first episode is especially a really cool intro to how modern fighter aircraft would compare to a Valkyrie.