I think that The Irresponsible Captain Tylor might have been the first anime series that I watched. I'd seen a few movies and specials before then, but not a long-run series. I encountered it in college; late at night, it appeared (subtitled) on The International Channel at some amazingly late hour, paired with Dragonball Z (which was not subtitled). DBZ was a bizarre soap opera that constantly promised imminent violence, but mainly consisted of glowing and glowering. ICT, on the other hand, was one of the funniest and most entertaining things available on television. It was as if someone had set out to create a show just for me: a science-fiction story, with space ships and battles and lasers and aliens, combined with a laissez-faire sensibility, sharp humor, and an explicit philosophy of "Do what you feel like, and don't worry, things will turn out."
There were a total of 26 episodes, and I managed to watch most of them, but not in order - studies sometimes got in the way, as did an occasional need to go to bed before 2AM. I think we started about a third of the way through the series, and caught most of what we missed when it repeated after the season ended. I've continued to think fondly of ICT since then, and recently treated myself to a re-watch - in order this time, completely from start to finish.
In the intervening ten years I've watched a LOT more anime. I've certainly seen shows that are prettier or more exciting. Still, I was impressed by how well ICT stands the test of time. It originally came out in the early 1990's, and apart from the opening credit sequence (which feels VERY 1980's, complete with a color-toned woman with big hair dancing like Paula Abdul), it doesn't feel dated. The art is (or at least looks) hand-drawn, but with high production quality and attention to detail. Characters actually move: Tylor slouches and stumbles across the bridge, the Marines stride, Harumi minces. The interior of the ship, where most of the series takes place, feels rather worn, but in a good way: you do get the impression they want to convey, that the Soyokaze is a rickety old beater that hasn't been cared for. Any time that they head off-ship, the backgrounds grow much more vibrant and pretty, whether it is the futuristic city-scapes on Earth, a verdant pastoral setting in a virtual reality simulator, or the gorgeous and ethereal sight of a nebula cloud.
So, the art is good, but what initially attracted me to this series and brought me back are the characters. The cast is even more varied and interesting than I had thought... I had remembered Tylor, Yuriko, and Yamomoto, but I had forgotten how prominently the doctor, Lt. Andressen, and the marines were. Over the course of the 26 episodes, you get to really know them well, and share some of the sense of camaraderie that blossoms on the Soyokaze.
To further develop that: Tylor is the center of the series, and the most amusing character, but this series isn't about one funny guy and 20 straight men. Tylor has a particular type of humor, but Yamomoto is hilarious in his over-the-top pursuit of honorable military virtues; the doctor gets laughs with his strange mixture of competence, drunkenness, and curiosity; the twins and the Akira-esque pilot have a great running gag of unwanted attention; Harumi and Andressen are great foils of toughness. And... had I just forgotten that there's a marine with a hockey mask named Jason?
I had remembered the strange shift in tone towards the end of the series. Or maybe it shouldn't be so strange; a good number of comedic Japanese anime seem to shift towards a more serious tone towards the conclusion. (Guu does it too, if memory serves correctly.) Still, Tylor was the first time I'd witnessed the phenomenon, and it felt a little weird when I first watched it. This time around, I was ready for it, and found that it was fine... the story isn't amusing during a couple of episodes, but it's still good, and it does set stuff up nicely for the end of the very last episode. If it was up to me (and maybe it's good that it wasn't), I'd have just made the series 25 episodes long, and combined numbers 24 and 25 into a single show. Too much moping for me. Still, saying that 4% of this show isn't enjoyable shouldn't count as criticism.
Be that as it may: ICT remains as funny, poppy, and weirdly inspiring as I remember. For a show that seems to parody ST:TNG, it's very much its own thing, and it's hard to think of what I can compare it to. If you haven't seen it yet, try to track it down and give it a watch; I hope you like it!