Anime Recommendations

[Branduil]

Cowboy Bebop, Escaflowne, and Evangelion are 90s classics.

For more recent shows,
Azumanga Daioh is the cream of the slice-of-lie crop. Very entertaining series about the everyday adventures of six high school girls.
Haibane Renmei is a very unique show with a wonderful soundtrack and art style.
Higurashi no Naku Koro ni- When They Cry A paranormal dramatic thriller set in a small, isolated Japanese village in the 80s, which enhances the horror by contrasting extreme cuteness with psycopathic violence.
Monster Simply unparalleled. A mystery/thriller placed in 90s Germany. One of the greatest villains of all time, and brilliant character writing.
Now and Then, Here and There An extremely dark but very good post-apocalyptic story, which actually deals seriously with issues like war, child soldiers, and rape.
Rozen Maiden It's about dolls who are alive and can fight. If you're not put off by the premise, it's actually very well-executed, balancing humor and drama well.
Gurren Lagann Really well-animated super robots.

 

[cattoy]

Azumanga Daioh is charming slice of life fluff. There's no extreme drama, violence or action. Still, it's entertaining as all heck. The characters are fun, their interplay ranges from goofy to hillarious. The artstyle is simplified and expressive. I recommend the subtitled version.

Planetes is a hard(ish) SF show about trash collectors that work in low earth orbit. It starts out as a fairly pedestrian workplace drama that starts to pick up speed and builds to a powerful crescendo at the end. The artwork is plain, but meticulous. It's not supposed to be pretty, but it doesn't detract from the storytelling.

Ranma 1/2 starts out very strong. They run out of steam some time later. Still, lots of good stuff before it gets repetitive.

Urusei Yatsura is the first series from Rumiko Takahashi. (creator of Ranma 1/2) I'm a fan of the show, but then again, I first watched it in the 80s. It's erratic and uneven, but the best episodes are amazing. I especially love the movies, but unless you've watched enough of the TV show, you won't get a lot of the references or in jokes. One of the movies was directed by Miyazaki.

Robot Carnival is a collection of shorts by various directors. All about robots. Some of them are thought provoking. Some of them are over the top action. Some of them are hillarious.

 

[ThirdWizard]

Personally, I'd recommend against Azumanga Daioh until one has more of an familiarity of Japanese humor and culture just like I'd recommend against Excel Saga until someone is fairly familiar with anime clichés.

 

[Aaron L]

Another vote for Tenchi Muyo! But only the original OVAs, the two tv series' are awful.


And I sitll love Dragonball Z.

 

[Arnwyn]

Another vote for Tenchi Muyo! But only the original OVAs, the two tv series' are awful.

Vice-versa for me. I found the OVAs to be terrible.

 

[Phoenix8008]

Some of my favorites that aren't on your list of having seen are:
-Record of Lodoss War (Very much a D&D anime. I loved it!)
-Guyver (Sci fi. Human in an alien powersuit vs. aliens. And the inspiration for a D&D Spelljammer item: the Bioseed Implant!
-Crying Freeman (modern day assassin with a concience. Very interesting.)
-Naruto (if you haven't heard of this already, then I'd be surprised. Kids in Ninja school but with some really neat long running plot threads.)
-Karas (a newer anime that I thought was really good and well done. I didn't know while watching it that it was only part I and it really left me wanting more. Part II, 'Karas: Revelation' is appearently due out very soon though so it might be safe to get into this one now.)

 

[Black Omega]

I will always have a soft spot for Bubble Gum Crisis. Not only does the name make more sense than it first seems, but when it was out I'd never watched anime until someone suggested I watch this. As it turned out because at the time I was playing a character that was the mirror of Pris, right down to the name. Good animation, not very tightly plotted, not the least because there was a change in storyline in the middle. something I don't usually see in an OAV series.

Ranma 1/2 is excellent for a few seasons, but I agree it's formulaic. But for a wild martial arts comedy, it's great fun.

 

[Samiko The Bard]

I also thought that Bubblegum Crisis was fairly decent. (the new one only, I have yet to see the old one.)

Bleach is another good choice, along with some others I have seen and liked:

Inuyasha, Blue Seed, Tenchi Muyo, Cowboy Bebop, DNAngel, Full Metal Panic, Oh, My Goddess, Outlaw Star, Full Metal Alchemist, Armitage, Pretear, Ceres, Please Teacher, and Gundam Wing or Gundam Seed.

I also HIGHLY recommend Fruits Basket, chances are both you and your wife will enjoy it.
Escaflowne rocks too.

 

[Deuce Traveler]

Maybe I missed it, but I was surprised to see no one mentioned Lain. I loved the visual and audial effects of that series.

 

[Merlion]

My three biggies:

Haibane-Renmei

Serial Experiments: Lain

Neon Genesis: Evangelion

Also Outlaw Star (from what I know of Cowboy Bebop, if you like it you'll probably like OS), RahXephon, Fullmetal Alchemist, Melody of Oblivion, FLCL, .hack//SIGN, Saiyuki, Get Backers, Paranoia Agent, also some that have already been mentioned such as Last Exile, Chrono Crusade, Bubblegum Crisis (at least the Tokyo 2040 version).

Yu-Yu Hakasho is sort of like DBZ but better, with more character development and (to me at least) more interesting storylines.

I'm liking Hellsing pretty well but it might be too violent for what your looking for.