disclaimers: I'm not going to be including anything I went through more then a few years ago, with the exception of Berserk since that is still relatively fresh in my head. The animes which would likely be on my list but I decided to hold off on actually putting on because of this are: Neon Genesis Evangelion, Full Metal Alchemist (original) and the manga (source material for Brotherhood), Video Experiments Lain, Akira (manga version), .Hack//sign, Cowboy Bebop, Samurai Champloo and The Slayers. A few of these I was hoping to revisit eventually in the future but until then they're put off to the side of this list to collect dust unfortunately >_> Same with anything that I haven't finished like LotGH and Princess Tutu (although I'll make exceptions if I've seen completed seasons that stand strong on their own for a show)
A few things that can effect my opinions or certain themes which may click particularly well with me to help give a bit of context. First off is something I've said a number of times before: A story needs to work with all it's parts as a whole, and if one part drags on or is weaker then it drags everything else down. Some arcs in a show can be weaker then others, but I hate storyline arcs or character arcs that feel pointless or like they're just trying to waste my time. I do however like good buildup. A story doesn't have to be deep and meaningful right away, infact many of my favorites are ones that appear quite simple at first and then spend a great deal of the series messing around with that initial appearance, which works particularly well in deconstruction stories. Things like animation and the OST can also have a large impact on my opinion of something, although the actual impact of those things can vary quite a bit. Almost everything on this list has tracks that I can either listen to on repeat for hours, or ones that can destroy me emotionally just by listening to it simply by making me remember the scene it played alongside. I prefer surreal type of animation the most, particularly the darker toned types that are full of large amounts of symbolism.
Theme is large since I like the story to feel like it has a purpose, and something that makes me feel like I have experienced something unique as I went through the story, and furthermore that the purpose of it is being conveyed effectively. This is particularly hard for longer animes to do since many of my favorites, and many of the ones I feel have the most purpose and meaning are much shorter. When I take a good 100+ episode anime it's much more difficult for it to stand up to a good 13 episode anime. Some themes do work better when spread over a longer period of time however, such as Breaking Bad (I know not an anime) and Berserk, I just feel it is much rarer for them to have a point and avoid the black hole of pointless storytelling that is known as fillers that are usually just there to waste time until the next arc. Also in terms of themes I like ones that push my understanding of a concept and deal with grey area and ideas that have multiple points of view and are hardly simple. Duality, love, memories, connections and staying true to ones self (or discovering ones true self) are all themes that I find especially drawn to.
15. Fate/Zero
14. Bakemonogatari
13. Kill La Kill
12. Psycho Pass
11. Welcome to the NHK
10. Baccano
9. Chuunibyou demo Koi ga Shitai!
8. Revolutionary Girl Utena
7. Clannad
6. Chihayafuru
5. Kaiba
4. Shin Sekai Yori
3. Zero Escape (Visual novel)
2. Berserk (manga)
1. Puella Magi Madoka Magica