See the initial 2000 entry for the full background. I'm doing this based on the show's start date and memorable is not the same as either good or significant; in fact there is one show in this list that stands out based on how much I viscerally disliked something it did. Date information comes from Wikipedia and Anime-Planet.

2004 is not the awesome year that 2002 was but it turns out to have a lot of plain good shows. The highs are not as high as 2002 but there's a lot more depth to the field, if that makes sense.

The biggest standouts (in preference order):

• Paranoia Agent: This show is amazing. I have no coherent words for it, especially ones that aren't spoilers. Episode 8 is a work of joyous art (and yes, I know that that's an odd thing to say given its contents).

• Windy Tales: Although this has an unconventional art style, I'm going to call it simply beautiful. It starts out with a flying cat (yes, really) and goes on from there to tell a series of affecting quiet stories. I love it unreasonably.

• Melody of Oblivion: What MoO does really well is be disturbingly weird. If the weirdness doesn't resonate with you, you're going to hate it; if it does, the entire show is a whole succession of wild rides. I loved the show, including all of the crazy mythological things it does, and think that it's underappreciated. And yes, I think it's supposed to be a somewhat uncomfortable watch all throughout, including the ending and the fanservice.

  (To pique your interest I'll note that it's written by Yoji Enokido, who also worked on Utena and Star Driver. This should give you a good idea of what you're in for.)

Standouts (in alphabetical order):

• Fantastic Children: The best description I can come up with is that this is an excellent children's science fiction adventure story, one that's good enough to be appreciated by all ages. Please note that I consider this strong praise.

• Gankutsuou: The Count of Monte Cristo: This oozes style and visual flair (some of it distracting), and the writing is decent and interesting; many people love it and rate it very highly. I can't, because late in the show's run it threw a melodramatic and gratuitous character death in my face and immediately lost me (and it's a death that doesn't occur in the original source material). That one moment made me want to throw the show against the wall and I dropped it on the spot.

  (I have to admit that even before the death totally irritated me I was sort of feeling that the show's stylishness was overcoming the story.)

• Ghost in the Shell: Stand Alone Complex 2nd Gig: I don't love this quite as much as I love the first season, but that merely makes it my second favorite Ghost in the Shell work. Everything good about the first season continues on in this, it's just not quite as shiny and new and exceptional this time around. The show is still excellent.

• Jubei-chan 2: This is an excellent followup to the first Jubei-chan (which can't really be called a 'season' because it's complete in and of itself). It reinforces what was good about Jubei-chan while adding its own layer of nice work and contributing its own set of great moments and subtle nuances.

  (Note that it can't be watched without having seen the first Jubei-chan.)

• My-HiME: This is Sunrise doing magical girls with mecha and carefully breaking any number of genre conventions in the process (but throwing in once-standard Sunrise elements like the midseason shock plot twist). The whole thing is simply a well put together package; characters, mecha designs, animation, story, everything. Some people hate the ending but I think it's fine and is perfectly appropriate for the show as a whole. I love the anti-cliche things that the show does with a number of the characters.

  (In many ways I think that this is Sunrise at the height of their powers and appeal.)

• Samurai Champloo: This show is a masterclass in how you do style and mix up your genres and settings, as Watanabe makes a whole series of crazy mashups work (primarily crossing classical samurai with hip-hop). One of the things that I always liked is how Mugen and Jin have such different (and fitting) sword styles.

• Uta Kata: The show starts out as a relatively normal magical girl story (of the old kind where the magical girl is given powers that she explores instead of given powers to fight things) and then goes into increasingly darker and more disturbing territory. This is not shock for the sake of shock; it's much more interesting and affecting than that.

Ordinarily memorable:

• Tweeny Witches aka Magical Girl Squad Arusu: Don't let the somewhat odd art style or setting put you off; this show has heart and a lot of appeal, and over the course of its run actually delivers a pretty darn epic adventure story.

  (This is also known as Mahou Shoujotai Arusu or sometimes Mahou Shoujo Tai.)

• Diebuster: This has one epic moment and a lot of decent work in the rest of it. It's Gainax trying hard and actually succeeding; while not as epic as the original Gunbuster it is a worthy followup.

• Le Portrait de Petit Cossette: This is one of the few works of more or less horror that I actually like (or liked when I saw it). It's spooky and disturbing and more psychological than anything else.

  (It's possible that I'd rate this lower if I rewatched it.)

• Magical Girl Lyrical Nanoha: The original TV series that launched what has become more or less an epic (once you roll in the successor TV series, the movies, the multiple manga, and so on). Nanoha more or less pioneered the otaku-focused fighting magical girls show and created a number of archetypes in the process. It has all sorts of epic beam-spam fights, a reasonably affecting storyline, some number of laughs, decent characters that have become classics, a few bits of unpleasant brutality when a character gets whipped, and some pieces of fanservice that are more than a bit creepy if you pay much attention to them.

  (I'd like to give it points for raising issues like Nanoha's increasing isolation from her friends, but the show never really goes anywhere with these issues.)

• Rozen Maiden: Underneath the flash and fire and dolls fighting each other, the first season is an affecting portrait of a shut-in recovering his spirit and willingness to interact with other people and the world.

• Tsukuyomi -Moon Phase-: One part charming, one part potentially irritating, one part vaguely disturbing, okay, this show has a lot of parts. It has a bunch of good characters, an understated romance between some people in the background, and a decently good story.

  Oh, and it sort of marks the start of Shaft's and Shinbo's wacky style of art and directing. Don't worry, it's relatively toned down and sensible here.

Honorable mentions, sometimes sort of:

• Bleach: For a while, this was a great shonen fighting show with some excellent characters. I still have fond memories of most of first year or so of episodes (up to the infamous first filler arc).

• Elfen Lied: This is notoriously bloody, graphically violent, graphical in general, and brutal. Take those out and there's nothing particularly novel here, but with them in the series is extremely memorable.

• Ghost in the Shell 2: Innocence: I feel sort of obliged to mention this somewhere even though I'm not really enthused about it in general. It's GitS, which means that it's pretty decent, and a GitS movie, which means that it looks amazing. It's a GitS movie by Oshii, which means that it's loaded with philosophy (some of it administered by blunt instruments).

• Gokusen: The granddaughter of a Yakuza boss becomes a teacher and of course is not at all bothered, scared, or impressed by the delinquents she winds up having as her students. This is basically a 'dedicated teacher' story (to steal the phrase from the Wikipedia entry) like eg GTO, but it's a well done and charming little series.

• Keroro Gunso aka Sgt. Frog: I gave up on this after a while, but it delivered both good entertainment and comedy that I actually liked. It understood that good comedy needs to be built around strong characters.

• Kurau Phantom Memory: This is a good science fiction show and character study that is somewhat marred by issues with the pacing. I remember it as well made and pretty exciting when it did action.

• 2x2 = Shinobuden: Funny and goofy and with a heart. One of the shows where the comedy works for me. Onsokumaru is a marvel who has to be heard to be appreciated; Norio Wakamoto really cuts loose and the result is glorious.

• This Ugly Yet Beautiful World: This was Gainax's 20th anniversary work and was theoretically supposed to be a showcase of them at their best. It didn't work out that way.

It looks like 2004 is the first year of the 00's where I can't spot anything obvious that I want to watch. Perhaps Sunabozu (aka Desert Punk), which I saw part of back in the days and which I've seen recommended since. I haven't seen Howl's Moving Castle yet but I've heard mixed reviews of it and I want to read the original book first.

Oh, and there's Futari wa Precure aka the starting point of the Precure juggernaut (which is still speeding along ten years later). I saw an episode or two back in the days and it was decent but not exceptional. I'd kind of like to see some Precure, but these days I'm probably not going get through an old year long series of any genre.

(A number of shows from 2004 that I've seen don't make this list for the usual reasons. Yes, believe it or not, I'm trimmed this instead of saying something about everything from 2004 that I've seen.)