It's hard for me to describe precisely why, because I remember shows in a way 'what I felt watching it' and not 'what I liked watching it' and I don't speak English too well, but I'll try because I prefer to read a few words about a show then just its title.
5 cm/s - closest to crying I've ever been
Animatrix - the world(s) they showed, the history behind the Matrix, hard to describe why exactly, but I felt this movie
Baccano! - great action, plenty of characters and the way the story gets into one piece was incredible
Danshi Kokousei no Nichijou - Everything was so out of place, but at the same time the characters in this show behaved 100 times closer to me and my friends than in any other anime I've seen, GTO, School Rumble and many more might've been on similar level of fun, but this one gets extra points for reminding me how I've had fun myself.
Ergo Proxy - the climate of loneliness, different cities made by other proxies, great OP and ED
GitS(1995) - I just love cyberpunk, but in this case I knew this is going to be one of my favourites during the scene when Motoko had a talk with Batou after diving.
NGE + EoE - I identified with Shinji and Rei was my first waifu xD I was sick watching it and don't remember the famous still image that lasted over a minute, but damn I watched it whole in one go because I just couldn't stop, it has this thing that makes Gainax productions a star out of 10 better than others(for me).
Place Promised in our Early Days - Shinkai's works may all be similar, but that means I'm gonna love all of them and I could very well put Voices of a Distant Star and Garden of Words in here too.
Serial Experiments Lain and Texhnolyze - I don't know why, I really don't. I just felt that I'm experiencing something special, listened to power lines with delight, saw how Lain walks on a shadow that looks like blood, how her world is weird, how she is abnormal, but all this things seemed to create something extremely interesting. You can apply comparable feels to Texhnolyze, even though the story was so much different, I instantly connected these two.
The Girl Who Leapt Through Time - a normal girl, I must add, but can't write much more without spoiling the movie
Tatami Galaxy - Masaaki Yuasa's show, my favourite, if you don't know the guy, you should check him out.
hard to leave out anything more than I already have, the list is in alphabetical order
I see Showdown has a good taste, I'll check animes from his list that I didn't see
